Box $ A $ contains $ 2 $ block and $ 3 $ red balls while box $ B $ contains $ 3 $ black and $ 4 $ red balls. Out of these two boxes one is selected at random and the probability of choosing box $ A $ is double that of box $ B $. If a red ball is drawn from the selected box, then the probability that it has come from box $ B $ is

Question

Box $ A $ contains $ 2 $ block and $ 3 $ red balls while box $ B $ contains $ 3 $ black and $ 4 $ red balls. Out of these two boxes one is selected at random and the probability of choosing box $ A $ is double that of box $ B $. If a red ball is drawn from the selected box, then the probability that it has come from box $ B $ is, $ \frac{21}{41} $, $ \frac{10}{31} $, $ \frac{12}{31} $, $ \frac{13}{41} $

MARKS App · Accepted Answer

P A = 2 B ⇒ P B = 1 3 P A = 2 3 Required Probability = 1 3 · 4 7 2 3 · 3 5 + 1 3 · 4 7 = 10 31 .

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