3. What is the probability of selecting a plain M&M candy, given that the candy is orange? 4. Are the events "selecting a Type A M&M candy" and "selecting a blue M&M candy" independent? Explain why or why not. 5. Are the events "selecting a brown M&M candy" and "selecting an Type B M&M candy" mutually exclusive? Explain why or why not.

7. Aaron purchased 19 video games. The defect rate for these types of video games is 1.8%. What is the probability that at least three of the video games he purchased are defective?

3.32 A pair of fair dice is tossed. Define the following events: A: B: {You will roll a 7.} (i.e., The sum of the dots on the up faces of the two dice is equal to 7.) {At least one of the two dice shows a 4.} a. Identify the sample points in the events A, B, An B, AUB, and Ac. b. Find P(A), P(B), P(A^ B), P(AUB), and P(A) by summing the probabilities of the appropriate sample points. c. Find P(AUB) using the additive rule. Compare your answer with that for the same event in part b. d. Are A and B mutually exclusive? Why?

A nationwide survey conducted by the National Cancer Society revealed the following information. Of 10,000 peoplesurveyed 3,200 were “heavy coffee drinkers”, and 160 of those surveyed had cancer of the pancreas. Of those who hadcancer of the pancreas, 132 were heavy coffee drinkers. Using the data in this survey, determine whether the events “beinga heavy coffee drinker” and “having cancer of the pancreas” are independent events.

7. State College is playing a rival team for the football championship. If State's first- string quarterback is healthy, State College has a 75% chance of winning. If they have to start their backup quarterback, their chances of winning drop to 40%. The team physician says that there are a 70% chance that the first-string quarterback will play. a. What is the probability that State will win that game? b. Suppose that you miss the game but you read in the headlines of Sunday's paper that State won. What is the probability that the second-string quarterback started?

1. You select a coin at random from your pocket. You replace the coin and select again. Are your selections independent events? Explain.