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Chapter 3: 3.88 (page 106)
In Example 5e, what is the conditional probability that the ith coin was selected given that the first n trials all result in heads?
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On the morning of September , the won–lost records of the three leading baseball teams in the Western Division of the National League were as follows:
Each team had games remaining. All of the Giants’ games were with the Dodgers, and the remaining games of the Braves were against the San Diego Padres. Suppose that the outcomes of all remaining games are independent and each game is equally likely to be won by either participant. For each team, what is the probability that it will win the division title? If two teams tie for first place, they have a playoff game, which each team has an equal chance of winning.
Let , and be events relating to the experiment of rolling a pair of dice.
(a) If localid="1647938016434" and localid="1647938126689" either prove that localid="1647938033174" or give a counterexample by defining events and for which that relationship is not true.
(b) If localid="1647938162035" and either prove that or give a counterexample by defining events and for which that relationship is not true. Hint: Let be the event that the sum of a pair of dice is ; let be the event that the first die lands on ; let be the event that the second die lands on .
A red die, a blue die, and a yellow die (all six-sided) are rolled. We are interested in the probability that the number appearing on the blue die is less than that appearing on the yellow die, which is less than that appearing on the red die. That is, with B, Y, and R denoting, respectively, the number appearing on the blue, yellow, and red die, we are interested in .
(a) What is the probability that no two of the dice land on the same number?
(b) Given that no two of the dice land on the same number, what is the conditional probability that ?
(c) What is ?
There are 3 coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?
Suppose we have 10 coins such that if the ith coin is flipped, heads will appear with probability i/10, i = 1, 2, ..., 10. When one of the coins is randomly selected and flipped, it shows heads. What is the conditional probability that it was the fifth coin
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