I need to determine x given the following conditions.
A and B are two events of Ω.
P(not A) = 3x
P(B) = 1/2
P(A or B) = 9x
P(A and B) = 3x
Here's what I thought of (but I know is wrong):
P(A or B) = 9x P(A) + P(B) = 9x 1 - P(not A) + 1/2 = 9x 1 - 3x + 1/2 = 9x x = 1/8
The answer is 0.1, but I can't get to it. I can't do the above because P(A or B) = P(A) + P(B)
can only be done if P(A and B) = 0
, and we are not told that here.
Any ideas? Thank you in advance.