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: Event A ⇒ P(A) = 0.16 Event B ⇒ P(B) = 0.09 Probability of event B given event A happening, P(B|A) = P(A∩B) / P(A) = 0.12
By the conditional probability, the probability of event A and event B happens together is given by: P(B|A) = P(A∩B) ÷ P(A) P(B|A) = P(A∩B) ÷ 0.16 0.12 = P(A∩B) ÷ 0.16 P(A∩B) = 0.12 × 0.16 P(A∩B) = 0.0192
When two events are independent, P(A) × P(B) = P(A∩B) so if P(A∩B) = 0.0192, then P(B) will be 0.0192 ÷ 0.16 = 0.12 (which take us back to P(B|A))
Since P(B|A) does not equal to P(B), event A and event B are not independent.
Answer: <span>Events A and B are not independent because P(B|A) ≠ P(B)</span>
