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  • If P(A)=4/5 , and , then P(B | A) is equal to A. 1|10 B. 1|8 C. 7|8 D. 17|20

If P(A)=\frac{4}{5} , and P(A \cap B)=\frac{7}{10} , then P(B | A) is equal to
A. 1|10
B. 1|8
C. 7|8
D. 17|20

Answers (1)

Given-  P(A)=\frac{4}{5} , and P(A \cap B)=\frac{7}{10}

\begin{aligned} &\text { As we know, }\\ &\mathrm{P}(\mathrm{B} \mid \mathrm{A}) \times \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{A} \cap \mathrm{B}) \quad[\text { Property of Conditional Probability] }\\ &P(B \mid A) \times \frac{4}{5}=\frac{7}{10}\\ &P(B \mid A)=\frac{7}{10} \times \frac{5}{4}\\ &P(B \mid A)=\frac{7}{8} \end{aligned}

Hence, Correct option is C

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