## sasogeek 4 years ago 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

1. across

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 $$P(B)$$.

2. sasogeek

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