Problem 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 \(7 ?\)
Problem 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?
Problem 4
The probability that you will win a game is \(0.45 .\) (a) If you play the game 80 times, what is the most likely number of wins? (b) What are the mean and variance of a binomial distribution with \(\mathrm{p}=0.45\) and \(\mathrm{N}=80 ?\)
Problem 5
A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?
Problem 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?
Problem 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?
Problem 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?
Problem 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?
Problem 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?
Problem 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 between 5 and 10 times (inclusive)? b. What is the probability that you will win the game at least 15 times? c. What is the probability that you will win the game at least 40 times? d. What is the most likely number of wins. e. What is the probability of obtaining the number of wins in d? Explain how you got each answer or show your work.
