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# 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 $P(B \cap \bar{C}$)

$\begin{array}{1 1}(A)\;0.20\\(B)\;0.17\\(C)\;0.37\\(D)\;0.57\end{array}$

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• $P(B \cap \bar{C})=P(B)-P(B \cap C)$
According to the venn diagram
$P(B \cap \bar{C})=P(B)-P(B \cap C)$------(1)
$P(B)=0.07+0.10+0.15=0.32$
$P(B \cap C)=0.15$
Substituting these in (1) we get
$P(B \cap \bar{C})=0.32-0.15$
$\Rightarrow 0.17$
Hence (B) is the correct answer.