If A and B are independent events such that $Pr(A)=1/3$ and $Pr(B)>0$, what is the value of $Pr(A$ $\cup$ $B^c$$|B)=?$
From what I can understand , if we use the conditional probability formula , the numerator will be $Pr(A$ $\cup$ $B^c$ $\cap$ $B)$ which will be $0$ and therefore the answer is $0$ however im not sure. Can someone confirm or tell me where im going wrong?
Best Answer
You can make a venn-diagramm.
If we now intersect this the marked area with $B$ then we obtain $A\cap B$.
Therefore $P((A\cup B^c)\cap B)=P(A\cap B)\stackrel{\textrm{ind.}}{=}P(A)\cdot P(B)$