3 Math 161A - Spring 2017 1. Suppose an individual is randomly selected from all adults living in the United States. Define the events A = the individual is CEO of an oil company, and B = the individual has an annual salary of over $100,000. Which one do you think is larger P (A|B) or P (B|A)? Explain your reasoning. 2. A box contains three black and five white balls. Three balls are selected one by one without replacement. What is the probability that the first ball is white, the second is black, and the third is white? 3. Two fair six-sided dice are rolled. What is the conditional probability that at least one lands on a four given that neither of them lands on a six? 4. A small treasure chest contains two drawers. Drawer I contains three gold and four silver coins and drawer II contains five silver and three gold coins. A drawer is randomly selected and from that drawer two coins are chosen at random (and without replacement). (a) What is the probability that the selected coins are gold and silver? (b) Given that the selected coins are gold and silver, what is the probability they came from drawer I? 5. One box contains five red balls and four green balls, and a second box contains six red balls and three green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the second box and placed in the first box. (a) What is the probability that a red ball is selected from the first box and a red ball is selected from the second box? (b) Put all balls back into their original positions and repeat the selection process. At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are identical to the numbers in the beginning? 6. Two fair six-sided dice are tossed simultaneously. (a) Are the events \"the dice land on the same number\" and \"the two numbers sum to more than seven\" independent? Support your answer with numerical evidence. (b) Are the events \"the dice land on different numbers\" and \"their sum is even\" independent? Support your answer with numerical evidence. 1