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Question Number 98201 by pranesh last updated on 12/Jun/20

Answered by Rio Michael last updated on 12/Jun/20

$$P\left(A\right)=0.4,P\left(B\right)=0.3,P(A\cup B)=0.6$$$$\mathrm{but}P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$$$$\Rightarrow 0.6=0.4+0.3-P(A\cap B)$$$$\Rightarrow -0.1=-P(A\cap B)\Rightarrow P(A\cap B)=0.1$$$$P\left(A\right)=P(A\cap B^{\prime })+P(A\cap B)$$$$\Rightarrow P(A\cap B^{\prime })=P\left(A\right)-P(A\cap B)=0.4-0.1=0.3$$$$\mathbf{Answers}:P(A\cap B)=0.1,P(B^{\prime }\cap A)=0.3$$

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