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1. How many three person committees can be chosen from a group of six people? 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can they finish the race if they won 1st, 2nd, 3rd and 4th place? 3. There are 6 things in a hat. How many ways can you pick 2 things from the hat at once?

1. How many three person committees can be chosen from a group of six people? 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can they finish the race if they won 1st, 2nd, 3rd and 4th place? 3. There are 6 things in a hat. How many ways can you pick 2 things from the hat at once?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. How many three person committees can be chosen from a group of six people? 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can they finish the race if they won 1st, 2nd, 3rd and 4th place? 3. There are 6 things in a hat. How many ways can you pick 2 things from the hat at once? 4. In how many ways can Dylan, Taylor, Sydney, Alyssa, Natalie, and Madison stand in line? 5. Sara has 10 different ribbons to wear in her hair. How many different ways could she arrange to wear the ribbons? 6. Given the following statistics, what is the probability that a woman has cancer if she has a positive mammogram result? One percent of women over 50 have breast cancer. • Ninety percent of women who have breast cancer test positive on mammograms. • Eight percent of women will have false positives. 7. One of two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2. A box is selected at random and a ball is selected at random from it. a. Given that the ball selected is red, what is the probability it was selected from the first box? b. Given that the ball selected is red, what is the probability it was selected from the second box? c. Compare the results in parts a) and b) and explain the answer.
Transcribed Image Text:1. How many three person committees can be chosen from a group of six people? 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can they finish the race if they won 1st, 2nd, 3rd and 4th place? 3. There are 6 things in a hat. How many ways can you pick 2 things from the hat at once? 4. In how many ways can Dylan, Taylor, Sydney, Alyssa, Natalie, and Madison stand in line? 5. Sara has 10 different ribbons to wear in her hair. How many different ways could she arrange to wear the ribbons? 6. Given the following statistics, what is the probability that a woman has cancer if she has a positive mammogram result? One percent of women over 50 have breast cancer. • Ninety percent of women who have breast cancer test positive on mammograms. • Eight percent of women will have false positives. 7. One of two boxes contains 4 red balls and 2 green balls and the second box contains 4 green and two red balls. By design, the probabilities of selecting box 1 or box 2 at random are 1/3 for box 1 and 2/3 for box 2. A box is selected at random and a ball is selected at random from it. a. Given that the ball selected is red, what is the probability it was selected from the first box? b. Given that the ball selected is red, what is the probability it was selected from the second box? c. Compare the results in parts a) and b) and explain the answer.
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