X. Given P(A) = 0.2, P(B) = 0.7, P(A | B) = 0.3, do the following. %3D %3D %3D (a) Compute P(A and B). (b) Compute P(A or B).

Dividing a Jackpot A game between two pIayers consists of tossing coin. Player A gets a point if the coin shows heads, and player B gets a point if it shows tails. The first player to get six points wins an $8000 jackpot. As it happens, the police raid the place when player A has five points and B has three points. After everyone has calmed down, how should the jackpot be divided between the two players? In other words, what is the probability of A winning (and that of B winning) if the game were to continue? The French mathematicians Pascal and Fermat corresponded about this problem, and both came to the same correct conclusion (though by very different reasoning's). Their friend Roberval disagreed with both of them. He argued that player A has probability of Winning, because the game can end in the four ways H, TH, TTH, TTT, and in three of these, A wins. Roberval’s reasoning was wrong. Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform this experiment 80 or more times, and estimate the probability that player A wins. Calculate the probability that player A wins. Compare with your estimate from part (a).

Telephone Marketing A mortgage company advertises its rates by making unsolicited telephone calls to random number. About 2% of the calls reach consumers who are interested in the company’s services. A telephone consultant can make 100 calls per evening shift. What is the probability that two or more calls will reach an interested party in one shift? How many calls does a consultant need to make to ensure at least a 0.5 probability of reaching one or more interested parties? [Hint: Use trial and error.]

In Example 8, what is the probability that an employee chosen at random has 30 or more years of service?