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  • Let P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13. Then P(A′|B) is equal to A. 6/13 B. 4/13 C. 4/9 D. 5/9

Let P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13. Then P(A′|B) is equal to
A. 6/13
B. 4/13
C. 4/9
D. 5/9

Answers (1)

Given-

P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13

\begin{aligned} &P\left(A^{\prime} \mid B\right)=\frac{P\left(A^{\prime} \cap B\right)}{P(B)}\\ &\text { From the above Venn diagram, }\\ &\frac{\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)}{\mathrm{P}(\mathrm{B})}=\frac{\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}\\ &\Rightarrow \frac{\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}=\frac{\frac{9}{13}-\frac{4}{13}}{\frac{9}{13}}\\ &\Rightarrow \frac{5}{13} \times \frac{13}{9}\\ &\Rightarrow \mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)=\frac{5}{9}\\ &\text { Hence, } \mathrm{P}\left(\mathrm{A}^{\prime} \mid \mathrm{B}\right)=\frac{5}{9} \end{aligned}

 

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