The probability of contamination in batch 1 of a drug (event A) is 0.16, and the probability of contamination in batch 2 of the drug (event B) is 0.09. The probability of contamination in batch 2, given that there was a contamination in batch 1, is 0.12. Given this information, which statement is true?

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

B.Events A and B are independent because P(A|B) ≠ P(A).

C.Events A and B are not independent because P(B|A) ≠ P(B).

D.Events A and B are not independent because P(A|B) = P(A).

Question

The probability of contamination in batch 1 of a drug (event A) is 0.16, and the probability of contamination in batch 2 of the drug (event B) is 0.09. The probability of contamination in batch 2, given that there was a contamination in batch 1, is 0.12. Given this information, which statement is true?

A.Events A and B are independent because P(B|A) = P(A).

B.Events A and B are independent because P(A|B) ≠ P(A).

C.Events A and B are not independent because P(B|A) ≠ P(B).

D.Events A and B are not independent because P(A|B) = P(A).

anonymous · Answer

C

mathmate · Answer

There are at least three ways to define independence: If one of the following conditions is true, A and B are independent. 1. P(A)*P(B)=P(A$\cap$B) 2. P(A|B)=P(A) 3. P(B|A)=P(B) Also, the contrapositive is equivalent, i.e. if one of the above conditions is not true, then A and B are not independent. Read more about it at: https://www.mathsisfun.com/data/probability-events-independent.html or https://en.wikipedia.org/wiki/Independence_(probability_theory)