Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is:

To solve this problem, we can use the concept of probability and combinations.

Step 1: Calculate the total number of ways to select 2 persons out of 13. This can be done using the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, and r is the number of items to choose.

So, the total number of ways to select 2 persons out of 13 is C(13, 2) = 13! / [(13-2)! * 2!] = 78.

Step 2: Calculate the number of ways to select 2 men out of 8. This is done because we are looking for the probability that at least one of the selected persons will be a woman. So, we need to find the probability of the opposite event (selecting 2 men) and subtract it from 1.

The number of ways to select 2 men out of 8 is C(8, 2) = 8! / [(8-2)! * 2!] = 28.

Step 3: Calculate the probability of selecting 2 men. This is done by dividing the number of ways to select 2 men by the total number of ways to select 2 persons.

So, the probability of selecting 2 men is 28 / 78 = 0.35897.

Step 4: Calculate the probability that at least one of the selected persons will be a woman. This is done by subtracting the probability of selecting 2 men from 1.

So, the probability that at least one of the selected persons will be a woman is 1 - 0.35897 = 0.64103.

Therefore, the probability that at least one of the selected persons will be a woman is approximately 0.641 or 64.1%.