# The accompanying venn diagram shows three events A,B and C,and also the probabilities of the various intersections (for instance $P(A \cap B)=0.07$).Determine $P(A\cup B)$

$\begin{array}{1 1}(A)\;0.45\\(B)\;0.35\\(C)\;0.75\\(D)\;0.50\end{array}$

Toolbox:
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
$P(A\cup B)=P(A)+P(B)-P(A\cap B)$-------(1)
According to venn diagram
$P(A)=0.20$
$P(B)=0.07+0.10+0.15=0.32$
$P(A \cap B)=0.07$
Substituting these values in (1) we get
$P(A\cup B)=0.20+0.32-0.07$
$\Rightarrow 0.45$
Hence (A) is the correct answer.