Question

The number of men and women wearing hats at a recent baseball game is recorded. The results are shown below. Hat No Hat Total Men 35 21 46 Women 10 32 42 Total 45 53 88 If one of these people at the baseball game is selected at random, find the probability that a) the person is a woman b) the person was wearing a hat. c) the person was wearing a hat, given that the person was a man. e) the person is a man, given that they were not wearing a hat.

Answer 1

The Hat No Hat data for men is erroneous as 35+21 = 56 (and not 46). We shall presume that 35 21 56 is the correct statistics.

The total number of men and women at the baseball game is 56+42 = 98. The total number of persons wearing hats is 35+10 = 45.

a). If one of these people at the baseball game is selected at random, the probability that the person is a woman is 42/98 = 0.428571428, say 0.43 (on rounding off to 2 decimal places).

b). ). If one of these people at the baseball game is selected at random, the person was wearing a hat is 45/98 = 0.459183673, say 0.46(on rounding off to 2 decimal places).

c). If one of these people at the baseball game is selected at random, the probability that the person was wearing a hat, given that the person was a man is 35/56 = 0.625.

e). If one of these people at the baseball game is selected at random, the probability that the person was not wearing a hat, given that the person was a man is   1-0.625 = 0.375.