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>
Since the total cost was $18.70 and there are ten in the pack, to find the price of one notebook you just need to divide the total cost by the amount of notebooks there are. So 18.70 divided by 10 is $1.87 for each notebook.
