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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 ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.
Options
`4/9`
`5/18`
`1/6`
`3/10`
Solution
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 draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is `underlinebb(5/18)`.
Explanation:
Given cooditions are
| 3R | 2R |
| 4B | 5B |
| 3W | 2W |
A : Drawn ball from boy II is black
B : Red ball transferred
Conditional probability is `P(B/A) = (p(A ∩ B))/(P(A))`
= `(3/9 xx 5/10)/(3/9 xx 5/10 + 4/9 xx 6/10 + 3/9 xx 5/10)`
= `15/(15 + 24 + 15)`
= `15/54`
= `5/18`
