A golfer has 12 golf shirts in his closet, 9 of which are white and the others b

Question

A golfer has 12 golf shirts in his closet, 9 of which are white and the others blue. He gets dressed in the dark, so he just grabs a golf shirt and puts it on. He plays golf on two days in a row and neither landers nor return the used shirts to the closet.

a. What is the probability that the first golf shirt selected was white?

b. What is the probability that the second golf shirt selected was blue given that the first one selected was white?

c. What is the probability that the first golf shirt selected was white and the second one selected was blue?

d. Write down the sample space by tree diagram, or by table, or by a set.

Explanation / Answer

(a) Probability that the first golf shirt was white = 9/12 = 0.75.

(b) Since, it is given that the first one was white, for the second day there will be 11 shirts out of which 3 are blue. So,

probability that the second golf shirt selected was blue given that the first one selected was white = 3/11 = 0.2727.

(c) probability that the first golf shirt selected was white and the second one selected was blue

= (9C1*3C1)/(12C2) = 9*3*2/12*11 = 0.409

(d) The sample in terms of set can be represented as {{white,white},{blue,white},{white,blue},{blue,blue}}, where the first element represents the shirt selected on first day and the second element represents the shirt selected on second day.

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