Question

Choose the correct alternative in the following question:

If A and B are two events associated to a random experiment such that $\mathrm{P}\left(A\cap B\right)=\frac{7}{10}\mathrm{and}\mathrm{P}\left(B\right)=\frac{17}{20}$, then P(A|B) =

$\left(\mathrm{a}\right)\frac{14}{17}\left(\mathrm{b}\right)\frac{17}{20}\left(\mathrm{c}\right)\frac{7}{8}\left(\mathrm{d}\right)\frac{1}{8}$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{P}\left(A\cap B\right)=\frac{7}{10}\mathrm{and}\mathrm{P}\left(B\right)=\frac{17}{20} \\ \mathrm{Now}, \\ \mathrm{P}\left(A|B\right)=\frac{\mathrm{P}\left(A\cap B\right)}{\mathrm{P}\left(B\right)} \\ =\frac{\left({\displaystyle \frac{7}{10}}\right)}{\left({\displaystyle \frac{17}{20}}\right)} \\ =\frac{7\times 20}{17\times 10} \\ =\frac{14}{17} \end{gathered}$$

Hence, the correct alternative is option (a).