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TAKS Objective 7 Questions 8-10 9/22/2012 7:23 PM 11.1 - Introduction to Probability 1 Grade Distribution 3rd 6th 7th A 8 1 2 B 10 8 9 C 2 5 6 D 4 7 0 F 1 5 5 No Show(s) 1 3 1 Avg 83.90 74.17 78.80 9/22/2012 7:23 PM 11.1 - Introduction to Probability 2 Question 8 Answer: G 9/22/2012 7:23 PM 11.1 - Introduction to Probability 3 Question 9 Answer: B 9/22/2012 7:23 PM 11.1 - Introduction to Probability 4 Question 10 Answer: J 9/22/2012 7:23 PM 11.1 - Introduction to Probability 5 Probability Section 11.1 9/22/2012 7:23 PM 11.1 - Introduction to Probability 6 Introduction • Probability: Likelihood that a certain outcome will happen. The probability of an event to happen is between 0 and 1. • 0: means that an event can not occur. (0%) • 1: means that an event is certain to occur (100%) • Sample Space: Considering a set, S, composed of a finite number of outcomes, which is likely to occur. • Event: An outcome in which the ratio of the number of outcomes will occur. Number of outcomes in event P Number of outcomes in sample space 9/22/2012 7:23 PM 11.1 - Introduction to Probability 7 Example 1 You are rolling a six-sided die whose sides are numbered from 1 to 6. Find the probability of: A) Rolling a 4. Number of outcomes in event P Number of outcomes in sample space Number of ways to roll a 4 P Number of ways to roll the die 1 P 6 9/22/2012 7:23 PM 11.1 - Introduction to Probability 8 Example 1 You are rolling a six-sided die whose sides are numbered from 1 to 6. Find the probability of: B. Rolling an odd number. Number of outcomes in event P Number of outcomes in sample space Number of ways to roll an odd number P Number of ways to roll the die 3 1 P 6 2 9/22/2012 7:23 PM 11.1 - Introduction to Probability 9 Example 1 You are rolling a six-sided die whose sides are numbered from 1 to 6. Find the probability of: C. Rolling a number less than 7. Number of outcomes in event P Number of outcomes in sample space Number of ways to roll less then 7 P Number of ways to roll the die 6 P 1 6 9/22/2012 7:23 PM 11.1 - Introduction to Probability 10 Example 1 You are rolling a six-sided die whose sides are numbered from 1 to 6. Find the probability of: D. Rolling 4 or 5. Number of outcomes in event P Number of outcomes in sample space OR add Number of ways to roll 4 or 5 P Number of ways to roll the die 2 1 P 6 3 9/22/2012 7:23 PM 11.1 - Introduction to Probability 11 Example 1 You are rolling a six-sided die whose sides are numbered from 1 to 6. Find the probability of: E. Rolling 4 AND then a 5. Number of outcomes in event P Number of outcomes in sample space Number of ways to roll 4 Number of ways to roll 5 P Number of ways to roll the die Number of ways to roll the die AND multiply 1 1 P 1 6 6 36 9/22/2012 7:23 PM 11.1 - Introduction to Probability 12 Example 2 You are rolling two six-sided die whose sides are numbered from 1 to 6. Here are the possibilities: 9/22/2012 7:23 PM 11.1 - Introduction to Probability 13 Example 2 You are rolling two six-sided die whose sides are numbered from 1 to 6. What is the probability if: • The sum of the numbers is 7. 1 6 1 • The sum of the numbers is 11. 1 18 • The sum of the numbers is 2. 36 15 • The sum of the numbers is at least 8. 36 • http://www.shodor.org/interactivate/activities/Ex pProbability/?version=1.5.0_06&browser=MSIE& vendor=Sun_Microsystems_Inc. 9/22/2012 7:23 PM 11.1 - Introduction to Probability 14 Example 3 • One marble is drawn at random from a bag containing 3 red marbles, 6 yellow marbles, and 9 blue marbles. Find the probability of each event: 1 • It is red. 6 • It is red or yellow. 1 2 2 • It is not yellow. 3 9/22/2012 7:23 PM 11.1 - Introduction to Probability 15 Example 4 • How many even 2-digit positive integers less than 50 are there? 20 9/22/2012 7:23 PM 11.1 - Introduction to Probability 16 Fundamental Counting Principle • Fundamental Counting Principle: If one event can occur in m ways and another in n ways, then the number of ways that both can occur is m • n. • This principle can be extended to three or more events. For example, if three events can occur m, n, and p ways, then the number of ways that all three can occur is m•n•p 9/22/2012 7:23 PM 11.1 - Introduction to Probability 17 Example 5 A certain deli offers 3 types of meat (ham, turkey, and roast beef) and 3 types of bread (white, wheat, and rye). Determine the different ways the deli offers: • Types of meat • Types of bread white ham on white ham wheat ham on wheat rye ham on rye white turkey on white turkey wheat turkey on wheat rye turkey on rye white roast beef on white wheat roast beef on wheat roast beef rye roast beef on rye 9/22/2012 7:23 PM 11.1 - Introduction to Probability 18 Example 6 If there are 10 choices for each digit and 26 choices for each letter, how many different license plates are possible if the digits and letters can be repeated? The first three choices are numbers, the last three choices are letters. • There are 10 choices for each digit and 26 choices for each letter. • Use the Fundamental Counting Principle to find the number of license plates... • Number of Plates = 10 • 10 • 10 • 26 • 26 • 26 17,576,000 different license plates 9/22/2012 7:23 PM 11.1 - Introduction to Probability 19 Example 7 If there are 10 choices for each digit and 26 choices for each letter, how many different license plates are possible if the digits and letters can NOT be repeated? The first three choices are numbers, the last three choices are letters. • There are 10 choices for each digit and 26 choices for each letter. • Use the Fundamental Counting Principle to find the number of license plates... • Number of Plates = 10 • 9 • 8 • 26 • 25 • 24 11,232,000 different license plates 9/22/2012 7:23 PM 11.1 - Introduction to Probability 20 Example 8 What is the probability of having a perfect 64-team NCAA bracket? (disregard seeding odds) 9/22/2012 7:23 PM 11.1 - Introduction to Probability 21 32 32 games and 2 teams = 2 (2 possible 1st round game winners to the power of 32 games) 9/22/2012 7:23 PM 11.1 - Introduction to Probability 22 16 games and 2 teams = 2 2 32 16 (2 possible 2nd round game winners to the power of 16 games) 9/22/2012 7:23 PM 11.1 - Introduction to Probability 23 8 games and 2 teams = 2 2 2 32 16 8 (2 possible Sweet 16 round game winners to the power of 8 games) 9/22/2012 7:23 PM 11.1 - Introduction to Probability 24 4 games and 2 teams = 2 2 2 2 32 16 8 4 (2 possible Elite Eight round game winners to the power of 4 games) 9/22/2012 7:23 PM 11.1 - Introduction to Probability 25 2 games and 2 teams = 2 2 2 2 2 32 16 8 4 (2 possible Final Four game winners to the power of 16 games) 2 9/22/2012 7:23 PM 11.1 - Introduction to Probability 26 1 game and 2 teams = 2 2 2 2 2 2 32 16 8 (2 possible Title game winners to the power of 1 game) 4 2 1 9/22/2012 7:23 PM 11.1 - Introduction to Probability 27 2 2 2 2 2 2 32 16 8 4 2 1 9,223,372,036,854,775,808 to 1 9/22/2012 7:23 PM 11.1 - Introduction to Probability 28 http://www.stat.yale.edu/~jay/News/WSJbb.pdf Assignment Complete Probability Worksheet 9/22/2012 7:23 PM 11.1 - Introduction to Probability 29