Independence and Conditional Probability

Question

In an experiment, the probability that event A occurs is 7/8,

and the probability that event B occurs is 5/9,

and the probability that event A  occurs given that event B occurs is 7/8.

.

Are A and B independent events? I am told the answer is YES, but my actual question follows:

P(A and B) = P(A)P(B) in order for the events to be independent.

But I am not sure how to read the equation. I was thinking that A and B meant addition, and P(A)P(B)meant multiplication, though that seems to be wrong. How do I easily interpret this equation and plug in the fractions from my example.

Thanks,

Brian

Answer 1

You are going to need to find P(A and B) given the equation:

P(A|B) P(B) = P(A and B), where P(A|B) is given as 7/8 and P(B) is given as 5/9.

7/8 * 5/9 = P(A and B)

35/72 = P(A and B)

P(A) is given as 5/9 so:

P(A) P(B) = 7/8 * 5/9 = 35/72

so P(A and B) = P(A) P(B) and thus A and B are independent