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Two people are selected at random from a group of eight women and ten men.
Find the probability of the following. (See Example 9. Round your answers to three decimal places.)
(a) both are men or both are women
(b) at least one is a woman
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8 women + 10 men comprise 18 people, altogether.
Of 18 people, the number of different pairs of people is
= = 9*17 = 153.
Of 8 women, the the number of different pairs of women is
= = 4*7 = 28.
Of 10 men, the the number of different pairs of men is
= = 5*9 = 45.
So, the answer to question (a) is
P = = = 0.477 (rounded).
To calculate the number of pairs, where at least one is woman, we subtract from 153
the number of pairs (man,man), which is 45
153-45 = 108.
To answer question (b), we relate this number of 108 to 153
P = = 0.706 (rounded).
Solved, with complete explanations.