Question

A bag contains 24 balls, out of which X are white. If one ball is drawn at random, the P(E) of drawing a white ball is Y. 12 more white balls are added to the bag. Now if a ball is drawn, from the bag, the P(E) of drawing a white ball is 5Y/3, find the value of X.

Answer 1

$$\begin{gathered} Given,Abagcontains24balls,outofwhichxarewhite.And,Probabilityofdrawingawhiteballisy. \\ So, \\ Probabilityofdrawingawhiteball=\frac{Numberofwhiteballs}{Totalnumberofballs} \\ \Rightarrow y=\frac{x}{24}......\left(1\right) \\ Now,12morewhiteballsareaddedtothebag.So, \\ Probabilityofdrawingawhiteball=\frac{Numberofwhiteballs}{Totalnumberofballs} \\ \Rightarrow \frac{5y}{3}=\frac{x+12}{24+12} \\ \Rightarrow \frac{5y}{3}=\frac{x+12}{36} \\ \Rightarrow 5y=\frac{x+12}{12} \\ \Rightarrow 5\times \frac{x}{24}=\frac{x+12}{12} \\ \Rightarrow 5x=2x+24 \\ \Rightarrow 3x=24 \\ \Rightarrow x=8 \end{gathered}$$
Hence, the value of x is 8.