JEE Main 2022 (Online) 24th June Morning ShiftQuestion 1
Bag $A$ contains $2$ white, $1$ black and $3$ red balls and bag $B$ contains $3$ black, $2$ red and $n$ white balls. One bag is chosen at random and $2$ balls drawn from it at random, are found to be $1$ red and $1$ black. If the probability that both balls come from Bag $A$ is $\frac{6}{11}$, then $n$ is equal to :
Probability
Solution
Bag A: $P(R,B)=\frac{3\cdot1}{15}=\frac15$. Bag B: $\frac{6}{\binom{n+5}2}=\frac{12}{(n+5)(n+4)}$. Bayes: $\frac{1/5}{1/5+12/((n+5)(n+4))}=\frac6{11}$ gives $(n+5)(n+4)=72$, $n=4$.