Which of the following are pairs of mutually exclusive events in the drawing of one card froma standard deck of 52? (a)A heart and a queen (b) A club and a red card. (c) An even number and a spade. (d) An ace and an even number. Which of the following are mutually exclusive outcomes in the rolling of two dice? (a) A total of 5 points and a 5 on one die. (b) A total of 7 points and an even number of points on both dice. (c) A total of 8 points and an odd number of points on both dice. (d) A total of 9 points and a 2 on one die. (e) A total of 10 points and a 4 on one die. Applications

Dividing a JackpotA game between two players consists of tossing a 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 8,000 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 Mathematician Pascal and Fermat corresponded about this problem, and both came to the same correct calculations though by very different reasonings. Their friend Roberval disagreed with both of them. He argued that player A has probability 34 of winning, because the game can end in the four ways H, TH, TTH, TTT and in three of these, A wins. Robervals reasoning was wrong. a Continue the game from the point at which it was interrupted, using either a coin or a modeling program. Perform the experiment 80 or more times, and estimate the probability that player A wins. bCalculate the probability that player A wins. Compare with your estimate from part a.

Bridge Hands What is the probability that a 13-card bridge hand consists of all cards from the same suit?