Question

Probability:
Two events A and B are such that \(\large P(A \) U \(\large B)=\frac{11}{15} \) and \(\large P(A)=\frac{1}{3} \) :
Find \(\large P(B) \) if the events A and B are
a. Mutually exclusive
b. Independent

Answer 1

Let \(A\) and \(B\) be mutually exclusive events.

Then the identity\[P(A\cup B)=P(A)\cup P(B)-P(A\cap B)\]becomes\[P(A\cup B)=P(A)\cup P(B).\]
Similarly, let \(A\) and \(B\) be independent events. Then the identity\[P(A\cup B)=P(A)\cup P(B)-P(A\cap B)\]becomes\[P(A\cup B)=P(A)\cup P(B)-P(A)P(B).\]
Finally, all you have to do is perform very simple algebra to find \(P(B)\).

Answer 2

Thank you:) though I figured the answer just a couple of minutes after asking. I'm glad you answered though, someone **MAY** need it. :P