Question

Five women and five men are waiting to be interviewed for a job. If they are all selected in random order, find the probability that the first interviewee will be a woman and the remaining ones will be alternate gender.

a) 1/9
b) 1/4
c) 1/5
d) 1/2

Answer 1

The probability that the first interviewee will be a woman and the subsequent interviewees will alternate in gender is 1/2.

Step-by-step explanation:

To find the probability that the first interviewee will be a woman followed by alternating genders, we first consider that there is a total of 10 people (5 women and 5 men), and we want a woman to be selected first. To determine this probability, we look at the total favorable outcomes divided by the total possible outcomes. There is a 1/2 chance (5 women out of 10 total candidates) that the first person selected is a woman.

Since the genders must alternate thereafter, and assuming the first person picked is a woman, there are 5 remaining men and 4 remaining women. The entire sequence is predetermined after a woman is selected first. Hence, the subsequent selections are not random. So, the probability the first person is a woman and the rest alternate in gender is simply the probability that the first interviewee is a woman, which is 1/2.