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There are three bags A,B,C ,Bag A contains two white balls and three black balls,Bag B contains four white balls and two black balls Bag C contains three white balls and two black balls.If a ball is drawn at random from randomly chosen bag,then findthe prabability that thedrawn is black ball

There are   three bags A,B,C ,Bag A contains two white balls and three black balls,Bag B contains four white balls and two black balls Bag C contains three white balls and two black balls.If a ball is drawn at random from randomly chosen bag,then findthe prabability that thedrawn is black ball 

Grade:12

1 Answers

Samyak Jain
333 Points
2 years ago
Probability of choosing any bag out of the three is 1/3  i.e. probability of choosing bag A is 1/3,
that of bag B is 1/3 and that of bag C is 1/3.
Now, probability of drawing a black ball out of 3 black and 2 white balls is 3/5.
So, probability of drawing a black ball from radomly chosen bag A is (1/3)(3/5).
Similarly, probability of drawing a black ball from radomly chosen bag B is (1/3)(2/6)
and that of drawing a black ball from radomly chosen bag C is (1/3)(2/5).
\therefore required probability is (1/3)(3/5) + (1/3)(2/6) + (1/3)(2/5)  =  (1/3)(3/5 + 2/6 + 2/5)
                                      =  (1/3) (4/3)  =  4/9.

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