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.
- 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
The closest answer is b. 0.745
- Pearl LLv 72 years ago
anything is possible
- llafferLv 72 years ago
There is a 100% probability that there is more to this question that you didn't supply.