Chapter 5 Exercises

Author(s)

Prerequisites

Selected answers

You may want to use the Binomial Calculator for some of these exercises.

1. (a) What is the probability of rolling a pair of dice and obtaining a total score of 9 or more? (b) What is the probability of rolling a pair of dice and obtaining a total score of 7? (Ch. 5.B)

2. A box contains four black pieces of cloth, two striped pieces, and six dotted pieces. A piece is selected randomly and then placed back in the box. A second piece is selected randomly. What is the probability that:

a) both pieces are dotted?
b) the first piece is black and the second piece is dotted?
c) one piece is black and one piece is striped?
(Ch. 5.B)

3. A card is drawn at random from a deck. (a) What is the probability that it is an ace or a king? (b) What is the probability that it is either a red card or a black card? (Ch. 5.B)

4. The probability that you will win a game is .45. (a) If you play the game 80 times, how many times would you expect to win? (b) What is the standard deviation of this distribution? (Ch. 5.F)

5. A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads? (Ch. 5.F)

6. When Susan and Jessica play a card game, Susan wins 60% of the time. If they play 9 games, what is the probability that Jessica will have won more games than Susan? (Ch. 5.F)

7. You flip a coin three times. (a) What is the probability of getting heads on only one of your flips? (b) What is the probability of getting heads on at least one flip? (Ch. 5.B & Ch. 5.F)

8. A test correctly identifies a disease in 95% of people who have it. It correctly identifies no disease in 94% of people who do not have it. In the population, 3% of the people have the disease. What is the probability that you have the disease if you tested positive? (Ch. 5.H)

9. A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). (a) What is the probability that one will be green and the other red? (b) What is the probability that one will be blue and the other yellow? (Ch. 5.B)

10. You roll a fair die five times, and you get a 6 each time. What is the probability that you get a 6 on the next roll? (Ch. 5.B)

11. You win a game if you roll a die and get a 2 or a 5. You play this game 60 times. (a) What is the probability that you win the game each time? (b) What is the mean of this distribution? (c) What is the variance of this distribution? (d) What is the probability that you will win the game at least 15 times? (e) What is the probability that you will win the game at least 40 times? (Ch. 5.F)

12. In a baseball game, Tommy gets a hit 30% of the time when facing this pitcher. Joey gets a hit 25% of the time. They are both coming up to bat this inning. (a) What is the probability that Joey or Tommy will get a hit? (b) What is the probability that neither player gets a hit? (c) What is the probability that they both get a hit? (Ch. 5.B)

13. An unfair coin has a probability of coming up heads of 0.65. The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places). (Ch. 5.F)

14. (a) What is the probability that you draw two cards from a deck and both of them are face cards (king, queen, or jack)? (b) What is the probability that you draw two cards from a deck and both of them are hearts? (Ch. 5.B)

15. True/False: It is more likely to get a pattern of HTHHHTHTTH than HHHHHHHHTT when you flip a coin 10 times. (Ch. 5.B)

16. True/False: Suppose that at your regular physical exam you test positive for a relatively rare disease. You will need to start taking medicine if you have the disease, so you ask your doctor about the accuracy of the test. It turns out that the test is 98% accurate. The probability that you have Disease X is therefore 0.98 and the probability that you do not have it is .02. (Ch. 5.H)


Questions from Case Studies:


The following questions are from the Diet and Health (DH) case study.

17. (a) (DH#1) What percentage of people on the AHA diet had some sort of illness or death?
(b) What is the probability that if you randomly selected a person on the AHA diet, he or she would have some sort of illness or death? (Ch. 5.B)
(c) If 3 people on the AHA diet are chosen at random, what is the probability that they will all be healthy? (Ch. 5.B)

18. (a) (DH#2) What percentage of people on the Mediterranean diet had some sort of illness or death?
(b) What is the probability that if you randomly selected a person on the Mediterranean diet, he or she would have some sort of illness or death? (Ch. 5.B)
(c) What is the probability that if you randomly selected a person on the Mediterranean diet, he or she would have cancer? (Ch. 5.B)
(d) If you randomly select five people from the Mediterranean diet, what is the probability that they would all be healthy? (Ch. 5.B)

Answers:

1) (a) 5/18 = .278

2) (b) 1/6 = .167

3) (a) 2/13 = .154

4) (b) 4.45

5) .164

7) (b) 7/8 = .875

9) (a) 2/19 = .105

11) (b) 20

12) (c) .075

14) (b) 1/17 = .0588

17) (c) .493

18) (b) .10