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Question Id : 11549 | Context :NIMCET 2023

Question

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ballsis 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 is red, is:
🎥 Video solution / Text Solution of this question is given below:

Conditional Probability – Bayes' Theorem

Given: One ball is transferred from Bag I to Bag II, and then a ball is drawn from Bag II and is black.

Goal: Find the probability that the transferred ball was red, given that a black ball was drawn.

Using Bayes' theorem: P(R|A)=P(R∩A)P(A)=310⋅510310⋅510+410⋅610+310⋅510=1554=518

✅ Final Answer: 518

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