Which statement is true about whether A and B are independent events? A and B are independent events because P (A∣B) = P (A) = 0.12. A and B are independent events because P (A∣B) = P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.12 and P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.375 and P (A) = 0.25

Question

Mathematics

Emanuel Lucero

8 November, 11:22

Which statement is true about whether A and B are independent events? A and B are independent events because P (A∣B) = P (A) = 0.12. A and B are independent events because P (A∣B) = P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.12 and P (A) = 0.25. A and B are not independent events because P (A∣B) = 0.375 and P (A) = 0.25

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Olivia Palmer · Answer 1

The events A and B are independent if the probability that event A occurs does not affect the probability that event B occurs.

A and B are independent if the equation P (A∩B) = P (A) P (B) holds true.

P (A∩B) is the probability that both event A and B occur.

Conditional probability is the probability of an event given that some other event first occurs.

P (B|A) = P (A∩B) / P (A)

In the case where events A and B are independent the conditional probability of event B given event A is simply the probability of event B, that is P (B).

Statement 1:A and B are independent events because P (A∣B) = P (A) = 0.12. This is true.

Statement 2: A and B are independent events because P (A∣B) = P (A) = 0.25.

This is true.

Statement 3: A and B are not independent events because P (A∣B) = 0.12 and P (A) = 0.25.

This is true.

Statement 4: A and B are not independent events because P (A∣B) = 0.375 and P (A) = 0.25

This is true.