Reply To: Question 47 — JEE Main 23 Jan 2026 S Ii
Solution
Event $\mathrm{E}_{1}$ : white ball is transferred
Event $\mathrm{E}_{2}$ : Black ball is transferred
\[
\mathrm{P}\left(\mathrm{E}_{1}\right)=\frac{6}{6+4}=\frac{3}{5}, \mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{4}{6+4}=\frac{2}{5}
\]
Event X : From bag A , white ball is drawn
\[
\begin{aligned}
& \mathrm{P}(\mathrm{X})=\mathrm{P}\left(\mathrm{E}_{1}\right) \mathrm{P}\left(\frac{\mathrm{X}}{\mathrm{E}_{1}}\right)+\mathrm{P}\left(\mathrm{E}_{2}\right) \mathrm{P}\left(\frac{\mathrm{X}}{\mathrm{E}_{2}}\right) \\
& =\frac{3}{5}\left(\frac{10}{18}\right)+\frac{2}{5}\left(\frac{9}{18}\right)=\frac{30+18}{5 \times 18}=\frac{8}{15}=\frac{\mathrm{p}}{\mathrm{q}} \\
& \therefore \mathrm{p}+\mathrm{q}=23 \text { Answer }(2)
\end{aligned}
\]