Question

The probability that a given urine sample analyzed in a pathology lab contains protein is 0.73 (event A). The probability that the urine sample contains the protein albumin is 0.58 (event B). The probability that a sample contains protein, given that albumin is detected, is 1.

Which statement is true?

Events A and B are dependent because P(A|B) = P(A).

Events A and B are dependent because P(A| B) P(B).

Events A and B are dependent because P(A|B) = P(A) + P(B).

Events A and B are dependent because P(A| B) P(A).

Events A and B are dependent because P(A|B) = P(A).

Answer 1

The correct answer among the choices provided is the second option. Events A and B are dependent because P(A|B) P(B). And from conditional probability, we have P(A|B) = P(AintersectionB) / P(B).
Therefore, P (AintersectionB) is equal to P(A|B) × P(B).