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Questions  >>  CBSE XII  >>  Math  >>  Probability
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Q)

A bag contains 4 white and 5 black balls.Another bag contains 9 white and 7 black balls.A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag.Find the probability that the ball drawn is white.

How to calculate p(A/E1)

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A)
Toolbox:
  • Let \(E_1\)=Whiteball transferred from bag1to bag2
  • \(E_2\)=Blackball transferred from bag1 to bag2
  • A=getting of white ball
  • P(A)=P(\(E_1\))P(\(A/E_1\))+P(\(E_2\))P(\(A/E_2\))
P(\(E_1\))=P(transferring white ball)
=\(\large\frac{4}{9}\)
P(\(E_2\))=P(transferring black ball)
=\(\large\frac{5}{9}\)
P(\(A/E_1\))=P(getting white from bag 2 when white ball is transfered)
=\(\large\frac{10}{17}\)
P(\(A/E_2\))=P(getting white from bag 2 when black ball is transfered)
=\(\large\frac{9}{17}\)
P(A)=\(\large\frac{4}{9}\times\)\(\large\frac{10}{17}\)+\(\large\frac{5}{9}\times\)\(\large\frac{9}{17}\)
=\(\large\frac{85}{153}\)

 

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