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? events a and b are independent because p(b|a) = p(a). events a and b are independent because p(a|b) ≠ p(a). events a and b are not independent because p(b|a) ≠ p(b). events a and b are not independent because p(a|b) = p(a). nextreset

We have:

P(A) = 0.16
P(B) = 0.09

If event A and event B are independent, then P(A) × P(B) = P(A∩B)
So, P(A∩B) should be 0.16 × 0.09 = 0.0144 if event A and event B are independent.

But we also have another probability related to event A and event B in our case, the conditional probability P(B|A) ⇒ Read, the probability of event B happening given event A is happening. The conditional probability P(B|A) is given by P(A∩B) ÷ P(A). We know the value of P(B|A) and P(A), so we can work out the value of P(A∩B) = P(B|A) × P(A) = 0.12 × 0.16 = 0.0192. This value of P(A∩B) is not as expected if event A and event B were independent. 

We need the value of P(B) to be equal to P(B|A) in order for the two events to be independent

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