Chapter 9 - Probability and Counting 212 1. A six-sided die is rolled twice. What is the probability of showing a 2 on the first roll and an odd number on the second roll? 2. A fair coin is flipped twice. What is the probability of showing heads on both flips? 3. A couple has three children. What is the probability that all three are girls? 4. Suppose that 21% of people own dogs. If you pick two people at random, what is the probability that they both own a dog? In your drawer you have 5 pairs of socks, 4 of which are white, and 1 1 tee shirts, 2 of which are white. If you randomly reach in and pull out a pair of socks and a tee shirt, what is the prob 6. Bert and Ernie each have a well-shuffled standard deck of 52 cards. They each draw one card from their own deck. Compute the probability that: a) Bert and Ernie both draw an Ace. b) Bert draws an Ace but Ernie does not. ) Neither Bert nor Ernie draws an Ace. d) Bert and Ernie both draw a heart. e) Bert gets a card that is not a Jack and Ernie draws a card that is not a heart. Chapter 9 - Probability and Counting 213 7. A jar contains 5 red marbles numbered 1 to 5 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability the marble is a) Even-numbered given that the marble is red. b) Red given that the marble is even-numbered. Compute the probability of flipping a coin and getting heads, given that the previous flip was tails. 9. Suppose a math class contains 25 students, 14 females (three of whom speak French) and 11 males (two of whom speak French). a) Compute the probability that a randomly selected student speaks French, given that the student is female. ) Compute the probability that a randomly selected student is male, given that the student speaks French. 10. A test was given to a group of students. The grades and gender are summarized below. Male Total Female 16 Total Suppose a student is chosen at random: a) Find the probability that the student was male given they earned an A. b) Find the probability that the student was male given they earned a C. c) Find the probability that the student was female given they earned a B. HW Day 9 - Adapted from Ch. 9 College Mathematics 1. A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. Let A be the event "the person is infected" and B be the event "the person tests positive". ) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B). b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B). 12. Tony buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 7 sugar cookies and 8 oatmeal cookies. What is the probability that Tony reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects a sugar cookie? 13. A math class consists of 25 students, 14 female and 11 male. Two students are selected at random to participate in a probability experiment. Compute the probability that ) a male is selected, then a female. b) a female is selected, then a male. c) two males are selected. d) two females are selected. e) no males are selected