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bag 1 contains 8 red and 2 black balls. bag 2 contains 7 red and 5 Black balls. one of the bags is chosen at random and a ball is drawn from it, which is found to be black. find the probability that the ball is drawn from bag 1.
Asked by janusingh736 | 13 Mar, 2024, 04:19: PM

Bag-1  B1 contains 8 red balls and 2 black balls .

Bag-2  B2 contains 7 red balls and 5 black balls .

Let P(B1) and P(B2) be the probability of selecting the bag-1 and bag-2 respectively to pick a ball.

P(B1) = P(B2) = 1/2

Let P( R | B1 ) be the probability of selectring red ball from bag-1.

Let P( R | B2 ) be the probability of selectring red ball from bag-2.

We get the above coditional probabilites as

P( R | B1 ) = 8/10

P( R | B2 ) = 7/12

Probabity of  randomly picked ball is red and is picked from bag-1 is P(B1 | R ) is

Answered by Thiyagarajan K | 14 Mar, 2024, 01:56: PM

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