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← JEE Main 2022 · 29 Jul · Shift 2
MathematicsSingle correct+4 / -1Question 16 of 90

JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 16

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Choose one option
Answer and worked solution

Official answer: B

Bayes. After transfer, P(black) is 510\frac5{10} (red or white moved) or 610\frac6{10} (black moved).

Posterior 310⋅510310⋅510+410⋅610+310⋅510=1554=518\dfrac{\frac3{10}\cdot\frac5{10}}{\frac3{10}\cdot\frac5{10}+\frac4{10}\cdot\frac6{10}+\frac3{10}\cdot\frac5{10}}=\dfrac{15}{54}=\dfrac5{18}.

(B)