Answer: The probability that no man will be selected is the number of ways that only women can be selected divided by the total number of combinations of candidates for the 2 data analyst positions. There are 2 ways to choose 2 women from the 2 available women, and there are C(4,2) = 6 ways to choose 2 candidates from the 3 men and 2 women, so the probability that no man will be selected is 2/6 = 1/3.
The probability that both men will get selected is the number of ways to choose 2 men from the 3 available men divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,2) = 3 ways to choose 2 men from the 3 available men, and there are C(5,2) = 10 ways to choose 2 candidates from the 3 men and 2 women, so the probability that both men will get selected is 3/10 = 3/5.
If Jyothi gets one more resume of a woman, there will be a total of 3 men and 3 women. The probability that only one man gets selected is the number of ways to choose 1 man and 1 woman from the 3 men and 3 women divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,1) * C(3,1) = 9 ways to choose 1 man and 1 woman, and there are C(6,2) = 15 ways to choose 2 candidates from the 3 men and 3 women, so the probability that only one man gets selected is 9/15 = 3/5.
Explanation: