A golfer has 12 golf shirts in his closet. Suppose 9 of these shirts are white and the others blue. He gets dressed in the dark, so he just grabs a shirt and puts it on. He plays golf two days in a row and does not do laundry.
What is the likelihood both shirts selected are white?
To find the likelihood that both shirts selected are white, we need to first determine the probability of drawing a white shirt on the first day and then the probability of drawing a white shirt again on the second day.
The probability of drawing a white shirt on the first day can be calculated as the ratio of the number of white shirts to the total number of shirts. In this case, there are 9 white shirts out of a total of 12 shirts, so the probability is 9/12.
Since the golfer does not do laundry between the two days, the number of shirts in the closet remains the same. Therefore, the probability of drawing a white shirt on the second day is also 9/12.
To find the likelihood of both shirts being white, we need to multiply the probabilities of both events occurring.
Probability of drawing a white shirt on the first day = 9/12
Probability of drawing a white shirt on the second day = 9/12
Probability of both shirts being white = (9/12) * (9/12) = 81/144 = 9/16
Therefore, the likelihood that both shirts selected are white is 9/16 or approximately 0.5625, or 56.25%.