Question

7 people show up to apply for jobs as cashiers at a discount store. Among 7 applicants, four are females. What is the probability that the first three lined up in the interview are all females if the order is chosen at random?

Answer 1

Answer:

11.43% probability that the first three lined up in the interview are all females if the order is chosen at random

Step-by-step explanation:

Initially, there are 7 applicants, 4 of which are female. So the probability of the first person lined up in the interview being a female is 4/7.

Now we suppose that a female has been chosen, which means that there are 6 applicants, 3 of which are female. So the probability of the second person lined up in the interview being a female is 3/6.

We suppose that the second choice was also a female. Now there are 5 applicants, 2 of which are female. So the probability of the third person lined up in the interview being a female is 2/5.

What is the probability that the first three lined up in the interview are all females if the order is chosen at random?

$P = \frac{4}{7}*\frac{3}{6}*\frac{2}{5} = 0.1143$

11.43% probability that the first three lined up in the interview are all females if the order is chosen at random