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Chapter 4: Q.4.14 (page 170)
A family has n children with probability where
(a) What proportion of families has no children?
(b) If each child is equally likely to be a boy or a girl (independently of each other), what proportion of families consists of k boys (and any number of girls)?
The answer of part (a) is
Part (b) is
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Four buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote the number of students who were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on her bus.
(a) Which of E[X] or E[Y] do you think is larger? Why?
(b) Compute E[X] and E[Y].
On a multiple-choice exam with possible answers for each of the questions, what is the probability that a student will get or more correct answers just by guessing?
In the game of Two-Finger Morra, players show or fingers and simultaneously guess the number of fingers their opponent will show. If only one of the players guesses correctly, he wins an amount (in dollars) equal to the sum of the fingers shown by him and his opponent. If both players guess correctly or if neither guesses correctly, then no money is exchanged. Consider a specified player, and denote by X the amount of money he wins in a single game of Two-Finger Morra.
(a) If each player acts independently of the other, and if each player makes his choice of the number of fingers he will hold up and the number he will guess that his opponent will hold up in such a way that each of the possibilities is equally likely, what are the possible values of and what are their associated probabilities?
(b) Suppose that each player acts independently of the other. If each player decides to hold up the same number of fingers that he guesses his opponent will hold up, and if each player is equally likely to hold up or fingers, what are the possible values of and their associated probabilities?
A salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability and his second will lead independently to a sale with probability . Any sale made is equally likely to be either for the deluxe model, which costs , or the standard model, which costs Determine the probability mass function of , the total dollar value of all sales
There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability Pi, i = 1, ... , N. Let T denote the number one need select to obtain at least one of each type. Compute P{T = n}.
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