0
$\begingroup$

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.

  • 0
    With $P(1-A)$ you mean $P(\text{not } A)$, I presume?2012-10-20
  • 0
    Indeed, will edit it.2012-10-20
  • 0
    $P(A\cup B) = 9x$ doesn't imply $P(A) + P(B) = 9x$ when $A\cap B\ne\emptyset$.2012-10-20
  • 0
    Really @FrenzYDT.? Damn, I was pretty sure about that.2012-10-20

1 Answers 1