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# 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)=$$\large\frac{4}{9}\times$$$$\large\frac{10}{17}$$+$$\large\frac{5}{9}\times$$$$\large\frac{9}{17}$$
=$$\large\frac{85}{153}$$