Question

100 voters were asked their opinion of two candidates X and Y running mayor

65 of them like X

55 of them like Y

25 of them like both

a-) what is the probability that someone likes neither

b-) What is the probability that someone likes exactly one candidate

c-) what is the probability that someone likes at least one candidate

Answer 1

a) We are given here that:

n(X) = 65,
n(Y) = 55,
n(both) = 25

n(at least 1) = n(X) + n(Y) - n(both) = 65 + 55 - 25 = 95
Therefore, n(likes neither) = Total - n(at least 1) = 200 - 95 = 105

Therefore probability = 105/200 = 0.525

Therefore 0.525 is the required probability here.

b) n(exactly 1) = n(at least 1) - n(both) = 95 - 25 = 70

Therefore probability = 70/200 = 0.35

Therefore 0.35 is the required probability here.

c) n(at least 1) = 95

Therefore probability = 95/200 = 0.475

Therefore 0.475 is the required probability here.