Question

If A and B are two events such that $P\left(A\right)=\frac{1}{4},P\left(B\right)=\frac{1}{2}$ and $P\left(A\cap B\right)=\frac{1}{8}$ find P$A\cup B$.

Answer 1

If $P\left(A\right)=\frac{1}{4}P\left(B\right)=\frac{1}{2}P(A\cap B)=\frac{1}{3}$

We know that

$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$P(A\cup B)=\frac{1}{2}+\frac{1}{4}-\frac{1}{8}$

$P(A\cup B)=\frac{4+2-1}{8}=\frac{5}{8}$

$P(A\cup B)=\frac{5}{8}$