Question

Is the number of members of Club X greater than the number of members of Club Y ? (1) Of the members of Club X, 20 percent are also members of Club Y. (2) Of the members of Club Y, 30 percent are also members of Club X.

Answer 1

Answer:

Yes

Step-by-step explanation:

The 20% of members of club X that are also members of club Y can be written as: P(Y/X) = 20% (that is, the probability of belonging to Y given that it belongs to X)

The 30% of members of club Y that are also members of club X can be written as: P(X/Y) = 30% (that is, the probability of belonging to X given that it belongs to Y)

The formula of conditional probability of A given B is  

P(A/B) = (A∩B) / P(A)

Where (A∩B) is the probability that both events A and B occur and P(A) is the probability of A.

Based on that, we can write,

P(Y/X) = P(Y∩X) / P(X) = 20 % = 0.2

P(X/Y) = P(Y∩X) / P(Y) = 30 % = 0.3

Clearing P(Y∩X) of both equations and equalizing,

P(Y/X).P(X) = P(X/Y).P(Y)

Moving terms ,

P(X) / P(Y) = P(X/Y) / P(Y/X) = 0.3 / 0.2 = 1.5

That is, P(X) is 1.5 times P(Y), which means that the amount of members of X is greater than the members of Y.