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PROBABILITY WORKSHEET I 1. Let E and F be events such that Pr(E ) .6, Pr(F ' ) .3 , and Pr(E F ) .8 . Find Pr(E F ). 2. Let S {s1 , s2 , s3 , s4 , s5 } be the sample space associated with an experiment having the following probability distribution. Outcome {s1} {s 2 } {s 3 } {s4 } {s5 } Probability 0.19 0.23 0.36 0.12 0.10 Given E {s1 , s2 , s3 }, F {s1 , s2 , s4 , s5 } and G {s 2 , s3 , s5 } , determine Pr[(E F ) ( F G)] . 3. While watching out their kitchen window, Mathia and Elias notice all the different birds using the birdbath over a period of an hour. Out of 143 birds, they count the following birds. Type of Bird Starlings Cedar Waxwings Purple Finches Sparrows Juncos Frequency 39 31 18 33 22 If a bird is chosen at random, find the probability that it is a. a junco b. a starling, a cedar waxwing or a purple finch c. not a starling 4. A hand of 9 cards is dealt from a well-shuffled deck of 54 cards (it includes the jokers). Find the probability that the hand contains 1 joker, 3 red cards, 4 clubs and 1 spades. 5. A hand of 10 cards is dealt from a well-shuffled deck of 52 cards. Find the probability that the hand contains at least 2 black cards. 6. A used car dealer has 150 used cars on his lot. The dealer knows that 30 of the cars are defective. If one of the 150 cars is selected at random, what is the probability that it is defective? 7. In a survey of 2140 teachers in a certain metropolitan area conducted by a nonprofit regarding teacher attitudes, the following data were obtained: 900 said that lack of parental support is a problem. 890 said that abused or neglected children are problems. 680 said that malnutrition or students in poor health is a problem. 120 said that lack of parental support and abused or neglected children are problems. 110 said that lack of parental support and malnutrition or poor health are problems. 140 said that abused or neglected children and malnutrition or poor health are problems. 40 said that all three issues are problems. Draw a Venn diagram and then find the probability that a teacher selected at random from this group said that lack of parental support is the only problem hampering a student's schooling? 8. A random selection of four books is made from a shelf containing six novels, five chemistry books, and three history books. Find the probability that two are novels, one is a chemistry book and one is a history book. 9. A new apartment complex advertises that it will give away three mopeds by a drawing from the first 50 students that sign a lease. Four friends are among the first 50 to sign. What is the probability that at least one of them will win a moped? 10. A pen holder holds ten pens, three of which do not write. If four pens are selected at random, a. find the probability that exactly two write. b. find the probability that at least one writes. 11. Of 400 college students, 120 are enrolled in math, 220 are enrolled in English, and 55 are enrolled in both. If a student is selected at random, find the probability that a. the student is enrolled in mathematics. b. the student is enrolled in mathematics or English. c. the student is enrolled in either mathematics or English, but not both. 12. In a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and brown eyes. If a child is selected at random, find the probability that the child has blonde hair or brown eyes. 13. Amber, a college senior, interviews with Acme Corp. and Mills, Inc. The probability of receiving an offer from Acme is 0.35, from Mills is 0.48, and from both is 0.15. Find the probability of receiving an offer from either Acme Corp. or Mills, Inc., but not both. 14. A survey of couples in a city found the following probabilities: The probability that the husband is employed is 0.85. The probability that the wife is employed is 0.60. The probability that both are employed is 0.55. A couple is selected at random. Find the probability that a. at least one of them is employed. b. neither is employed. 15. Three people are selected from a group of seven men and five women. Find the probability that a. all three are men. b. two are women and one is a man. 16. A survey to correlate class (freshman, sophomore, junior, senior) that a student is in with his/her political leanings of conservative or liberal was given to students at a certain college. a) What is the sample space for this experiment? b) Describe event E1 = “conservative” as a subset of the sample space. c) Describe the event E2 = “junior” as a subset of the sample space. 17. Suppose the odds of rain tomorrow are 5 to 3. What is the probability that rain will occur tomorrow? 18. Joey feels that the probability of getting an A on his anatomy exam is 0.71. What are his odds of getting an A on his anatomy exam? 19. Given S = {1, 2, 3, 4, 5, 6}; E = {1, 2}; F = {2, 3}; and G = {1, 5, 6}. Are E G and E'F ' mutually exclusive? 20. Given Pr(E) = 0.5, Pr(F)=0.3, and Pr(E∩F) = 0.1. Determine if E and F are independent events? ANSWERS 1. Since we are trying to find the probability of the intersection of E and F, we cannot use a Venn diagram. This means we need to use the formula, PrE F PrE PrF PrE F ; however, we don’t know Pr(F ) . We can find it -- Pr( F ) 1 Pr( F ' ) . .8 = .6 + .7 - PrE F PrE F = .5 2. E F {s1 , s2 } , F G {s 2, s5 } ; E F ( F G) {s1 , s 2 , s5 } ; PrE F ( F G) 0.19 + 0.23 + 0.10 = 0.52 3. a. 22/143 b. (39 + 31 + 18)/143 = 88/143 = 8/13 c. 1 – (39/143) = 104/143 = 8/11 C (2,1) * C (26 ,3) * C (13,4) * C (13,1) 48334000 4. = .009 C (54 ,9) 5317936260 C (26 ,0) * C (26 ,10 ) C (26 ,1) * C (26 ,9) 86550035 5. 1 1 1 .0055 .9945 C (52 ,10 ) 1582002422 0 C (30 ,1) * C (120 ,0) 30 1 6. C (150 ,1) 150 5 7. U PS A/NC 710 80 670 710/2140 40 70 100 470 M/PH C (6,2) * C (5,1) * C (3,1) 225 8. .2248 C (14 ,4) 1001 9. Pr(at least one friend will win a moped) = Pr(1 friend) + Pr(2 friends) + Pr(3 friends) = C (4,0) * C (46 ,3) 15180 4420 221 1 – Pr(0 friends) = 1 1 .2255 C (50 ,3) 19600 19600 980 C (7,2) * C (3,2) 63 3 10a. Pr(exactly two pens write) = =.3 C (10 ,4) 210 10 b. Pr(at least one writes) = Pr(1 writes) + Pr(2 write) + Pr(3 write) + Pr(4 write) = C (3,4) 1 – Pr(0 write) = 1 not possible = 1 – 0 = 1 C (10 ,4) 11. a. 120/400 b. (65+55+165)/400 = 285/400 M E c. (65+165)/400 = 230/400 65 55 165 115 12. BH BE (6+4+10)/35 = 20/35 6 4 10 15 13. A M .2 + .33 = .53 .20 .15 .33 .32 14. H W a. .3 + .55 + .05 = .9 .3 .55 .05 b. 1 - .9 = .1 .1 C (7,3) * C (5,0) 35 7 C (7,1) * C (5,2) 70 7 15. a. .159 b. .318 C (12 ,3) 220 44 C (12 ,3) 220 22 16. a.){ (freshman, conservative); (freshman, liberal); (sophomore, conservative); (sophomore, liberal); (junior, conservative); (junior, liberal); (senior, conservative); (senior, liberal)} b.) { (freshman, conservative); (sophomore, conservative); (junior, conservative); (senior, conservative)} c.) { (junior conservative); (junior liberal)} 5 5 17. Pr (rain tomorrow) = 53 8 .71 .71 71 18. odds of getting an A on anatomy exam: 71 to 29 1 .71 .29 29 19. ( E G) ( E 'G' ) {5,6} so no, they are not mutually exclusive 20. Not independent

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posted: | 7/30/2012 |

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