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

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