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 ______.

विकल्प

• `4/9`

• `5/18`

• `1/6`

• `3/10`

Answer 1

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`