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# What is the probability that at most 2 of the applicants will be female?

Previous research by a human resources consultancy has shown that 30% of applications for senior executive positions in the finance sector are women. Assume that the number of women who apply for senior executive positions can be modelled using a binomial distribution. A leading bank has received 6 applications for their advertised senior executive position.

a 0.500

b 0.745

c 0.571

d 0.429

e 0.666

### 3 Answers

- PuzzlingLv 72 years agoFavorite Answer
Use the binomial probability formula:

P(X = k) = C(n,k) * p^k * q^(n-k)

n : number of "trials" (6)

k : number of desired successes (0, 1 or 2)

p : probability of success (0.3)

q : probability of failure (1-p = 0.7)

So just figure out the probability of exactly 0, 1 or 2 women applicants and add them up.

P(X=0) = C(6,0) * 0.3^0 * 0.7^6 = 0.117649

P(X=1) = C(6,1) * 0.3^1 * 0.7^5 = 0.302526

P(X=2) = C(6,2) * 0.3^2 * 0.7^4 = 0.324135

The sum is 0.74431

Answer:

The closest answer is b. 0.745

thanks