A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one women will be selected is _______ (round off to 2 decimal places).

Answer :

Correct answer is : 0.93

There are 5 men and 3 women. Company is hiring to fill four managerial vacancies.

Probability that at least one woman will be selected = 1 - Probability that no woman is selected

Probability that no woman is selected = $\frac{{}^5{C}_4{\times }^3{C}_0}{{}^8{C}_4}=\frac{5\times 1}{70}=\frac{5}{70}$

Probability that at least one woman will be selected = 1 - Probability that no woman is selected = 1 - (5/70) = 65/70 = 0.93