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.

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

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