Question

a university has a total of 320 professors and 105 of them are women. what is the probability that a randomly selected professor from this university is a A. woman B.man ? do these two probabilities add up to 1.0? if yes, why?

Answer 1

Probability = Favorable Outcomes / Total Outcomes

Total Outcomes = 320

(A) P(Woman)

Favorable Outcomes = 105

Therefore the required probability = 105 / 320 = 21/64 = 0.3821

(B) P(Man)

Favorable Outcomes = 320 - 105 = 215

Therefore the required probability = 215 / 320 = 43/64 = 0.6719

(C) Yes, the sum of the probabilities (0.3821 + 0.6719) is equal to 1.

This is because a randomly chosen person can either be a man or a woman.

Probability of being a woman and the probability of being a man are mutually exclusive events i.e the intersection of the 2 events P( Man and Woman) = 0.