Can anyone help me with this proof? I'm completely lost.
Assume A and B are two events such that P(A and B) = P(A) P(B). Consider a third event C. Is it necessarily the case that P(A and B | C) = P(A | C) P(B | C)? If so, prove it. If not, give examples of A, B, and C such that one would reasonably expect that P(A and B) = P(A) P(B) but P(A and B | C) P(A | C) P(B | C).
Toss two dice, one red and the other green. Let A be the event that 3 appears on the red die; B is the event that 5 appears on the green die, and C is the event that sum of the two dice is 8. Note that P(A|C)=(1/5) and P(AB|C)=(1/5).
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Posted - 09/17/2007 : 02:37:44
