VIEWS: 18 PAGES: 21 POSTED ON: 3/15/2013
Probability 1. Gary has 1 red apple, 2 green apples, and 3 yellow apples in a sack. He also has 3 packages of peanuts, 1 package of almonds, and 2 packages of cashews in another sack. If he reaches into each sack without looking, what is the probability that he will grab a yellow apple and a package of almonds? A. B. C. D. 2. June is making a necklace for her friend out of beads. There is a one jar containing 1 blue bead and 5 green beads, and another jar containing 1 yellow bead and 3 brown beads. If she reaches in without looking and draws a bead from each jar, what is the probability that she will draw one blue bead and one yellow bead? A. B. C. D. 3. Daniel has 1 blue pencil and 5 yellow pencils in his backpack. He also has 2 pink erasers, 4 tan erasers, and 3 gray erasers in his backpack. If Daniel randomly selects one pencil and one eraser from his backpack, what is the probability that he will select a yellow pencil and a pink eraser? A. B. C. D. 4. Katie is trick or treating. The man answering the door holds out two bags. In one bag, there are 3 bars of dark chocolate and 1 bar of white chocolate. In the other bag, there are 3 pieces of strawberry licorice, 1 piece of cherry licorice, and 1 piece of orange licorice. If Katie gets to randomly draw one piece of candy from each bag, what is the probability that she will get a bar of white chocolate and a piece of orange licorice? A. B. C. D. 5. There are two jars. One jar contains 2 red gumballs, 3 green gumballs, and 1 yellow gumball. The other jar contains 2 blue balloons and 3 purple balloons. Jeff randomly draws one gumball and then one balloon. What is the probability that he will draw a yellow gumball and a purple balloon? 1 2 1 1 A. B. C. D. 15 15 5 10 6. Chris has a bag of four apples. Three of the apples are red and one of them is green. He also has a bag with two sandwiches. One of the sandwiches is ham and the other is turkey. If he reaches into both bags without looking, what is the probability that he will grab a red apple and a turkey sandwich? 3 1 1 2 A. B. C. D. 8 2 8 3 7. Jeff has 2 red pens and 4 blue pens in his backpack. He also has 1 yellow highlighter and 4 green highlighters in his backpack. If he reaches into his backpack and grabs one pen and one highlighter without looking, what is the probability that he will grab a blue pen and a yellow highlighter? 8 2 1 5 A. B. C. D. 15 15 15 11 8. An experiment is broken up into two parts. In the first part of the experiment a penny is tossed in the air. If the coin lands on heads, then the coin is flipped a second time. If the coin lands on tails, then a six-sided die is rolled. What is the probability of getting two tails? 5 B. 0 1 3 A. C. D. 11 12 4 9. There are 2 red gumdrops and 3 green gumdrops in a small jar. Also, 4 pieces of butterscotch candy and 1 piece of cinnamon candy are in another jar. If Craig draws one piece of candy from each jar without looking, what's the probability that he will get a red gumdrop and a piece of cinnamon candy? 3 4 3 2 A. B. C. D. 10 25 25 25 10. An experiment is broken up into two parts. In the first part of the experiment, a six sided die is rolled. In the second part of the experiment, a dime is tossed in the air. What is the probability of getting a 3 and tails as the outcome? 1 1 1 1 A. B. C. D. 2 6 12 24 11. Todd forgot the first two numbers of his locker combination. The numbers can be any number 1 through 6. What is the probability that he will guess the first number incorrectly and the second number incorrectly? 5 25 5 1 A. B. C. D. 36 36 6 36 12. Bobby is taking a multiple-choice history test. He has decided to randomly guess on the first two questions. On each question there are 4 answer choices. What is the probability that he answers the first question incorrectly and the second question incorrectly? 2 3 9 1 A. B. C. D. 3 16 16 16 13. A single six-sided die is rolled twice. What is the probability of rolling an odd number on the first roll and an even number on the second roll? 1 1 1 1 A. B. C. D. 36 6 12 4 14. There are two jars. One jar has 2 orange marbles and 3 red marbles. The other jar has 1 blue marble and 4 green marbles. If Jeff randomly draws one marble from each jar, what is the probability that he will draw a red marble and a blue marble? 8 12 2 3 A. B. C. D. 25 25 25 25 15. Bob has a coin cup with four $1 tokens and two $5 tokens in it. He also has two $10 tokens and one $25 token in his pocket. He randomly draws a token from the cup, and then randomly draws a token from his pocket. What is the probability that he will draw $26 in tokens? 2 4 1 1 A. B. C. D. 9 9 2 9 16. An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. What is the probability that the sum of the dots is 7 or 11? 5 1 7 2 A. B. C. D. 18 9 36 9 17. A parking lot has seventy parking spaces numbered from 1 to 70. There are no cars in the parking lot when Jillian pulls in and randomly parks. What is the probability that the number on the parking space where she parks is greater than or equal to 30? 29 41 70 70 A. B. C. D. 70 70 29 41 18. The following balls are placed in an urn: 6 red, 4 yellow, 5 blue, and 3 green. One ball is randomly drawn from the urn. What is the probability that the ball is either yellow or green? 1 7 7 7 A. B. C. D. 9 36 11 18 19. An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. What is the probability that the sum of the dots is divisible by 4? 5 7 1 1 A. B. C. D. 18 12 5 4 20. In an experiment a six-sided die is rolled a number of times. The results are shown below. Number Rolled Number of Times Rolled 1 8 2 4 3 5 4 9 5 6 6 5 Based on these results, what is the experimental probability of rolling either a 2 or 3? A. 8/37 B. 9/37 C. 9/29 D. 9/32 21. A card is randomly drawn from an ordinary deck of playing cards. What is the probability that the card is a king or a diamond? P( K D) 0.31 C. P( K D) 0.33 E. P( K D) 0.13 B. P( K D) 0.53 D. P( K D) 0.35 22. Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts. Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the probability that Sam randomly chooses a shirt that is blue or has stripes? A. P( B S ) 0.33 C. P( B S ) 0.69 E. P( B S ) 0.27 B. P( B S ) 0.8 D. P( B S ) 1.46 23. David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the the movie will be a comedy or a movie that he has not seen? A. P(C S ) 0.44 C. P(C S ) 0.61 E. P(C S ) 0.56 B. P(C S ) 0.39 D. P(C S ) 0.83 24. In a group of 294 students, 130 are seniors and 121 are males. Exactly one-half of seniors are females. If a student is randomly selected, what is the probability that the student is a senior or a female? A. P( S F ) 0.63 C. P( S F ) 0.81 E. P( S F ) 1.25 B. P( S F ) 0.22 D. P( S F ) 0.59 25. The contingency table below gives the counts of students by activities and gender. Band Sports Debate Total Male 105 320 7 432 Female 105 160 14 279 Total 210 480 21 711 If a student is randomly selected, what is the probability that a student is female or plays sports? A. P( F S ) 0.16 C. P( F S ) 0.84 E. P( F S ) 1.3 B. P( F S ) 0.74 D. P( F S ) 0.26 26. Harold has one bag of different-colored, same-size chips and one bag of different-colored, same-size marbles. In the first bag there are 4 blue chips, 5 red chips, and 3 black chips. In the second bag there are 5 green marbles, 4 blue marbles, and 3 red marbles. What is the probability that he will pull a blue chip and a blue marble from the bags? 1 1 1 1 A. B. C. D. 9 3 4 6 27. Frank is conducting an experiment. He has one bag of different colored, same-size chips and one bag of ten same-size chips numbered 1-10. In the first bag there are 4 blue chips, 5 red chips, and 3 black chips. If he pulls one chip out of each bag, what is the probability that he will pull a black chip and an even number? 1 1 1 1 A. B. C. D. 4 8 3 2 28. Sarah has one bag of ten same-size chips numbered 1-10 and one six-sided die. What is the probability that she will pull an odd number from the bag and roll an odd number on the die? 1 1 1 2 A. B. C. D. 6 4 2 3 29. Richard conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on tails and the die will land on an even number? 1 1 1 1 A. B. C. D. 8 6 4 12 30. Johan conducting an experiment. Every time he flips a fair two-sided coin, he also rolls a six-sided die. What is the probability that the coin will land on either heads or tails and the die will land on an even number? 1 1 1 1 A. B. C. D. 6 8 2 4 31. Julia conducting an experiment. Every time she flips a fair two-sided coin, she also rolls a six-sided die. What is the probability that the coin will land on heads and the die will land on a number? 1 1 1 1 A. B. C. D. 2 6 4 12 32. Holly is flipping a coin and pulling a marble from a bag. There are 4 white marbles, 2 blue marbles, and 5 green marbles, all of the same size, in the bag. What is the probability that the coin lands on heads and she pulls a green marble from the bag? 1 3 5 6 A. B. C. D. 4 11 22 13 33. Audrey has a bag of similar-sized red and green grapes. There are 12 red grapes and 13 green grapes in the bag. If the first 7 grapes she ate were green what is the probability that the 8th grapes she eats is green and the 9th grape she eats is red? 3 4 1 3 A. B. C. D. 11 17 4 50 34. Marli has one bag of different colored, same-size chips. There are 4 blue chips, 5 red chips, and 3 black chips. What is the probability that she will pull a blue chip and without replacement pull another blue chip? 3 1 1 1 A. B. C. D. 11 4 3 11 35. Brandon is rolling two six-sided dice. What is the probability that one die lands on an even number and the other die lands on an odd number? 1 1 1 1 A. B. C. D. 8 2 3 4 36. Doreen is flipping two fair coins. What is the probability that both coins land on heads? 1 1 1 1 A. B. C. D. 4 2 3 8 37. Mark has a standard deck of 52 cards and a fair two-sided coin. What is the probability that he will pull a jack from the deck of cards and toss the coin to land on heads? 1 1 1 1 A. B. C. D. 26 8 13 2 38. Gretta is rolling a die and pulling a marble from a bag. There are 4 white marbles, 3 blue marbles, and 4 green marbles, all of the same size, in the bag. What is the probability that she rolls a 4 and she pulls a blue marble from the bag? 1 1 3 4 A. B. C. D. 22 6 11 17 39. Kayla has a standard deck of 52 cards and a six-sided die. What is the probability that she will pull a diamond from the deck of cards and roll a 2? 3 1 1 1 A. B. C. D. 26 24 4 6 40. Courtney and Alan are conducting an experiment. Every time Courtney flips a fair two-sided coin, Alan rolls a six-sided die. What is the probability that the coin will land on heads and the die will land on 2? 2 1 1 1 A. B. C. D. 3 6 12 8 20. B Answers 21. A 22. B 1. D 23. C 2. D 24. C 3. A 25. C 4. C 26. A 5. D 27. B 6. A 28. B 7. B 29. C 8. B 30. C 9. D 31. A 10. C 32. C 11. B 33. B 12. C 34. D 13. D 35. D 14. D 36. A 15. A 37. A 16. D 38. A 17. B 39. B 18. D 40. C 19. D Explanations 1. The first sack contains 1 red apple, 2 green apples, and 3 yellow apples. The second sack contains 3 packages of peanuts, 1 package of almonds, and 2 packages of cashews. The probability of Gary randomly grabbing a yellow apple and a package of almonds is calculated below. 2. The first jar contains 1 blue bead and 5 green beads. The second jar contains 1 yellow bead and 3 brown beads. The probability of June randomly drawing one blue bead and one yellow bead is calculated below. 3. In Daniel's backpack, he has 1 blue pencil and 5 yellow pencils, as well as 2 pink erasers, 4 tan erasers, and 3 gray erasers. The probability of Daniel randomly selecting a yellow pencil and a pink eraser from his backpack is calculated below. 4. One bag contains 3 dark chocolate bars and 1 white chocolate bar. The other bag contains 3 pieces of strawberry licorice, 1 piece of cherry licorice, and 1 piece of orange licorice. The probability of Katie randomly drawing a bar of white chocolate and a piece of orange licorice is calculated below. 5. The first jar contains 2 red gumballs, 3 green gumballs, and 1 yellow gumball. The second jar contains 2 blue balloons and 3 purple balloons. The probability of Jeff drawing a yellow gumball and a purple balloon is calculated below. 6. One bag contains 3 red apples and 1 green apple. The other bag contains 1 ham sandwich and 1 turkey sandwich. The probability of Chris randomly drawing a red apple and a turkey sandwich is calculated below. 7. In Jeff's backpack, he has 2 red pens and 4 blue pens, as well as 1 yellow highlighter and 4 green highlighters. The probability of Jeff randomly grabbing a blue pen and a yellow highlighter from his backpack is calculated below. 8. When conducting an experiment with dependent events, it is helpful to draw a probability tree for the experiment. Since there are no ways of getting two tails, the probability is 0. 9. The first jar contains 2 red gumdrops and 3 green gumdrops. The second jar contains 4 pieces of butterscotch candy and 1 piece of cinnamon candy. The probability of Craig drawing a red gumdrop and a piece of cinnamon candy is calculated below. 10. Since each of the six sides of the die has an equal chance of turning up on each roll, the probability of landing on a particular number during any roll of the die is . Since each flip of the coin has an equal chance of landing on heads or tails, the probability of landing on heads is equal to the probability of landing on tails, which is . Therefore, the probability of getting a 3 and tails as the outcome is calculated below. 11. For each number in the combination, there is 1 correct number and 5 incorrect numbers. The probability of Todd randomly guessing the first two numbers in his locker combination, and getting the first number incorrect and the second number incorrect, is calculated below. 12. For each question, there is 1 correct answer choice and 3 incorrect answer choices. The probability of Bobby randomly guessing on the first two questions and getting the first question incorrect and the second question incorrect is calculated below. 13. The even numbers on a die are 2, 4, and 6, and the odd numbers on a die are 1, 3, and 5. The probability of rolling an odd number followed by an even number is calculated below. 14. The first jar contains 2 orange marbles and 3 red marbles. The second jar contains 1 blue marble and 4 green marbles. The probability of Jeff drawing a red marble and a blue marble is calculated below. 15. The cup contains four $1 tokens and two $5 tokens. Bob has two $10 tokens and one $25 token in his pocket. To get $26 in tokens, Bob must draw a $1 token from the cup and a $25 token from his pocket. The probability of Bob drawing $26 in tokens is calculated below. 16. There are 6 combinations that sum to 7 and 2 combinations that sum to 11. This gives a total of 8 combinations out of a possible 36 that sum to 7 or 11. So, the probability that the sum of the dots is 7 or 11 is 8 out of 36, or . 17. There are a total of 70 parking spaces. Of those 70 parking spaces, there are 41 with the number 30 or greater. Therefore, the probability that the number on the parking space Jillian randomly chooses has a number that is greater than or equal to 30 is 41 out of 70, or . 18. There are a total of 18 balls in the urn. Of those 18 balls, there are 4 yellow and 3 green, for a total of 7 balls that are either yellow or green. Therefore, the probability that the ball drawn is either yellow or green is 7 out of 18, or . 19. The sums of 4, 8, and 12 are all divisible by 4. There are 3 combinations that sum to 4, 5 combinations that sum to 8, and 1 combination that sums to 12. Thus, there are 9 combinations out of a possible 36 that are divisible by 4. So, the probability that the sum is divisible by 4 is 9 out of 36, or . 20. The probability of rolling a 2 is 4/37. The probability of rolling a 3 is 5/37. 4 /37 + 5/37 = 9/37 = 9/37 21. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur. Define the events. The question asks for the probability that either event occurs; therefore, the addition rule must be applied. Rewrite the addition rule for the given events, K and D. Calculate P(K), P(D), and P(K D). Find P(K). There are 52 total cards in an ordinary deck, and 4 of the total cards are kings. Find P(D). There are 52 total cards in an ordinary deck, and 13 of the total cards are diamonds. Find P(K D). There are 52 total cards in an ordinary deck, and there is only 1 diamond that is also a king. Substitute P(K), P(D), and P(K D) into the addition rule formula and simplify to obtain the final answer. 22. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur. Define the events. The question asks for the probability that either event occurs; therefore, the addition rule must be applied. Rewrite the addition rule for the given events, B and S. Calculate P(B), P(S), and P(B S). Find P(B). There are 15 total shirts in the closet, and 8 of the shirts are blue. Find P(S). There are 15 total shirts in the closet, and 9 of the total shirts have stripes. Find P(B S). There are 15 total shirts in the closet, and there are 5 shirts that are blue and have stripes. Substitute P(B), P(S), and P(B S) into the addition rule formula and simplify to obtain the final answer. 23. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur. Define the events. The question asks for the probability that either event occurs; therefore, the addition rule must be applied. Rewrite the addition rule for the given events, C and S. Calculate P(C), P(S), and P(C S). Find P(C). There are 18 total movies, and 7 of the movies are comedies. Find P(S). There are 18 total movies, and David has not seen 6 of the movies available. Find P(C S). There are 18 total movies, and David has not seen 2 of the comedies. Substitute P(C), P(S), and P(C S) into the addition rule formula and simplify to obtain the final answer. 24. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur. Define the events. The question asks for the probability that either event occurs; therefore, the addition rule must be applied. Rewrite the addition rule for the given events, S and F. Calculate P(S), P(F), and P(S F). Find P(S). There are 294 total students, and 130 of the students are seniors. Find P(F). There are 294 total students, and 121 of the total students are males. To calculate the number of females, subtract: 294 - 121 = 173. There are 173 females. Find P(S F). There are 294 total students, and one-half of the total seniors are female. To calculate the number of female seniors, multiply: 1/2(130) = 65. There are 65 female seniors. Substitute P(S), P(F), and P(S F) into the addition rule formula and simplify to obtain the final answer. 25. Given events A and B, use the following formula, defined as the addition rule, to find the probability that A or B will occur. Define the events. The question asks for the probability that either event occurs; therefore, the addition rule must be applied. Rewrite the addition rule for the given events, F and S. Calculate P(F), P(S), and P(F S). Find P(F). There are 711 total students, and 279 of the students are female. Find P(S). There are 711 total students, and 480 of the students play sports. Find P(F S). There are 711 total students, and 160 of the students are females who play sports. Substitute P(F), P(S), and P(F S) into the addition rule formula and simplify to obtain the final answer. 26. To find the probability of these two events happening at the same time, first find the individual probability of each. There are 12 colored chips in the first bag, 4 blue chips, 5 red chips, and 3 black chips. So, the probability of Harold picking out a blue chip is or . There are 12 colored marbles in the second bag. So, the probability of him picking blue marble is or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of a blue chip × probability of a blue marble = probability of both × = So, the probability of both events happening is . 27. To find the probability of these two events happening at the same time, first find the individual probability of each. There are 12 colored chips in the first bag, 4 blue chips, 5 red chips, and 3 black chips. So, the probability of Frank picking out a black chip is or . There are ten chips in the second bag, each numbered from 1-10 without a number being repeated. So, the probability of Frank picking an even number or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of black × probability of even = probability of both × = So, the probability of both events happening is . 28. To find the probability of these two events happening at the same time, first find the individual probability of each. There are ten chips in the second bag, each numbered from 1-10 without a number being repeated. So, the probability of Sarah pulling out an odd chip is or . There are six sides to the die that Sarah is rolling, each side with a number from one to six without any number being repeated. So, the probability of Sarah rolling an odd number or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of odd × probability of odd = probability of both × = So, the probability of both events happening is . 29. To find the probability of these two events happening at the same time, first find the individual probability of each. There are two sides to the coin Richard is flipping, one heads and one tails. So, the probability of him flipping the coin and it landing on tails is . There are six sides to the die that he is rolling, each side with a number from one to six without any number being repeated. So, the probability of him rolling an even number is or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of tails × probability of even = probability of both × = So, the probability of both events happening is . 30. To find the probability of these two events happening at the same time, first find the individual probability of each. There are two sides to the coin Johan is flipping, one heads and one tails. So, the probability of him flipping the coin and it landing on either heads or tails is or 1. There are six sides to the die that he is rolling, each side with a number from one to six without any number being repeated. So, the probability of him rolling an even number is or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of heads or tails × probability of even = probability of both × = So, the probability of both events happening is . 31. To find the probability of these two events happening at the same time, first find the individual probability of each. There are two sides to the coin Julia is flipping, one heads and one tails. So, the probability of her flipping the coin and it landing on heads is . There are six sides to the die that she is rolling, each side with a number from one to six without any number being repeated. So, the probability of her rolling a number is or 1. To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of heads × probability of a number = probability of both × = So, the probability of both events happening is . 32. To find the probability of these two events happening at the same time, first find the individual probability of each. The probability of coin landing on heads is . The probability of Holly pulling a green marble out of the bag is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of heads × probability of green = probability of both × = So, the probability of both events happening is . 33. To find the probability of this happening, first find the individual probability of each. There are 25 grapes total to start, 13 green and 12 red. If Audrey already ate 7 green grapes, there are 18 total grapes left, 6 green and 12 red. So, the probability of the 8th grape Audrey eats being green is or . The probability of 9th grape Audrey eats being red is . To find the compound probability of these events happening, multiply the probability of each event by the other. probability of 8th grape being green × probability of 9th grape being red = probability of both × = So, the probability of both events happening is . 34. To find the probability of these two events happening, first find the individual probability of each. There are 12 colored chips in the bag, 4 blue chips, 5 red chips, and 3 black chips. So, the probability of Marli picking out a blue chip is or . Since Marli does not replace the chip that she picked, there are 11 colored chips left in the bag. So, the probability of her picking blue chip again is . To find the compound probability of these events happening, multiply the probability of each event by the other. probability of a blue chip × probability of another blue chip = probability of both × = So, the probability of both events happening is . 35. To find the probability of these two events happening at the same time, first find the individual probability of each. The probability of first die landing on an even number is or . The probability of the second die landing on an odd number is or . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of even × probability of odd = probability of both × = So, the probability of both events happening is . 36. To find the probability of these two events happening at the same time, first find the individual probability of each. The probability of first coin landing on heads is . The probability of the second coin landing on heads is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of heads × probability of heads = probability of both × = So, the probability of both events happening is . 37. To find the probability of these two events happening at the same time, first find the individual probability of each. There are 52 cards in the deck Mark has and 4 of them are jacks. So, the probability of him pulling a jack is or . There are two sides to the coin he is flipping, one heads and one tails. So, the probability of him tossing the coin and it landing on heads is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of jack × probability of heads = probability of both × = So, the probability of both events happening is . 38. To find the probability of these two events happening at the same time, first find the individual probability of each. The probability of Gretta rolling a 4 is . The probability of her pulling a blue marble out of the bag is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of 4 × probability of blue = probability of both × = So, the probability of both events happening is . 39. To find the probability of these two events happening at the same time, first find the individual probability of each. There are 52 cards in the deck Kayla has and 13 of them are diamonds. So, the probability of her pulling a diamond is or . There are six sides to the die that she is rolling, each side with a number from one to six without any number being repeated. So, the probability of her rolling a 2 is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of diamond × probability of a 2 = probability of both × = So, the probability of both events happening is . 40. To find the probability of these two events happening at the same time, first find the individual probability of each. There are two sides to the coin Courtney is flipping, one heads and one tails. So, the probability of her flipping the coin and it landing on heads is . There are six sides to the die that Alan is rolling, each side with a number from one to six without any number being repeated. So, the probability of him rolling a 2 is . To find the compound probability of these events happening at the same time, multiply the probability of each event by the other. probability of heads × probability of 2 = probability of both × = So, the probability of both events happening is .