Boy or Girl paradox The following pair of questions appeared

Boy or Girl\' paradox. The following pair of questions appeared in a column by Martin Gardner in Scientific American in 1959.Be sure carefully justify your answers. Mr.jones has two children. The older child a girl. What is the probability that both children are girls? Mr.Smith has two children. At least one of them is a boy. What is the probability that both children are boys? (10 points) In a warehouse, up to 6 pallets of product A are kept in inventory at a given time. Therefore, the sample space S of the number of the number of pallets in stock is S={0,1,2,3,4,5,6} At the start of the day, if there are 3 or fewer pallets of A in stock, then an order is placed with the supplier. Write the event E that corresponds to needing to place an order for A on a randomly selected day. (15 points) Poker hands. After one-pair. the next most common hands are two-pair and three-of-a-kind: Two-pair: Two cards have one rank, two cards have another rank, and the remaining card has a third rank. e.g{2 2 5 5 k } Three-of-a-kind: Three cards have one rank and the remaining two cards have two other ranks e.g{2 2 2 5 k } Calculate the probability of each type of hand. Which is more likely? (15 points) Ignoring leap days, the days of the year can be numbered 1 to 365. Assume that birthdays are equally likely to fall on any day of the year. Consider a group of n people, of which you are not a member. An element of the sample space om will be a sequence of n birthdays (one for each person). Define the probability function P for om Carefully describe the subset of om that corresponds to each of the following events: \"someone in the group share your birthday\" \"some two people in the group share a birthday\"

Solution

1.Mr. Jones has two children. Th eolder is girl .

The sample space associated with this is { (G,B), (G,G)}

The probability that both children are girls = 1/2

b. Mr. Smith has two children . One of them is a boy.

The sample space associated with this is {(B,G), (B,B), (G,B)}

Probability that both children are boys = 1/3 ( (B,B) is only the favorable event)

As per chegg rules, ask one question in one post.

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