JEE Main 2022 · 24 Jun · Shift 1 · Mathematics Q4

← JEE Main 2022 · 24 Jun · Shift 1

MathematicsSingle correct+4 / -1Question 4 of 90

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 $\dfrac6{11}$ , then $n$ is equal to ______.

Answer and worked solution

Official answer: C

Likelihoods. From bag A (2W, 1B, 3R): $P(\text{1R,1B})=\dfrac{3\cdot1}{\binom62}=\dfrac15$ . From bag B (3B, 2R, $n$ W): $P=\dfrac{2\cdot3}{\binom{n+5}2}=\dfrac6{\binom{n+5}2}$ .

Bayes. $\dfrac{1/5}{1/5+6/\binom{n+5}2}=\dfrac6{11}$ gives $\dfrac{11}5=\dfrac65+\dfrac{36}{\binom{n+5}2}$ , so $\binom{n+5}2=36$ .

Solve. $(n+5)(n+4)=72$ , so $n=4$ .

(C)

Topics:Bayes' theorem Combinations

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JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 4