Help me clear up this probability problem please?

Question

If p(AnB)=p(A)*p(B) only when the two are dependent, how do you know if they are independent. And how do you solve for p(AnB) if the are dependent.

Answer 1

I'm no probability expert, but I think what you've stated is the normal definition of what it means for A and B to be independent. The intuitive idea is that A and B are independent if the the occurance of A does not affect the probability of B and vice versa.

In general, you have the relation:

P(AnB)/P(B) = P(A|B)

I think this is called Bayes's Theorem or something like that. In words it says that the probability of A and B over the probability of B equals the probability of A given B. So

P(AnB) = P(B)*P(A|B)

Note that when A is independent of B, that is the probability of A is unaffected by the occurance or nonoccurance of B, P(A|B) = P(A), and this formula simplifies to the one you have.

Answer 2

5s 8h 10c 6b 11r There are 40 finished, so the prob of finding out on a activities e book is 5/40 (a million/8) reckoning on whether the 1st e book is replaced, the risk of finding out on a baby's or historic previous is: with replace: 10+8=18, so 18/40 (9/20) with out replace: 10+8=18, so 18/39 (6/13)