Hello, blackZ!
I'll do the first one . . .
Since are independent,
. . we have, for example:
On the left side we have:
. .
. . . . . . . .
On the right side we have:
. .
. . . . . . . .
Suppose that A, B and C are independent events and P(C) ≠ 0. Prove:
a) P (A ∩ B | C) = P(A | C) P(B | C)
b) P (A ∪ B | C) = P(A | C) + P(B | C) - P (A ∩ B | C)
My book only this formula to proved the above question.
p(A | B) =(A ∩ B)/ P(B)
I dont know how to deal with 3 constants?
Any help?
Thanks
Thanks for the (a).
For (b), I simplified the right side to P(A)+P(B) - P(A)P(B)
I am not sure what UNION and CONDITIONAL probability means when A,B and C are independent? Is it the same as INTERSECTION and CONDITIONAL?
Thanks