Answer:
Yes
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.