If a joint relative frequency is 0.25 and the marginal relative frequency is 0.5, what is the conditional relative frequency?

• A. 0.5
• B. 0.25
• C. 0.125
• D. 0.75

Answer: (A)

The concept here is how to find a conditional relative frequency using the overlap and the subgroup’s total. The formula is P(A|B) = P(A ∩ B) / P(B). You’re given the joint relative frequency P(A ∩ B) = 0.25 and the marginal relative frequency P(B) = 0.5. So P(A|B) = 0.25 / 0.5 = 0.5. This means, among the outcomes where B occurs, half of them are also in A. The other options don’t fit because they wouldn’t match dividing the joint by the marginal; for instance, 0.25 would be the joint itself (as if P(B) were 1), 0.125 would require a different P(B), and 0.75 would exceed what’s possible given the joint portion within B.