A bag contrains 4 white and 5 black blls. 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.
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Here, `W_(1)` = {4 white balls} and `B_(1)`={5 black balls}
and `W_(2)` = {9white balls} and `B_(2)` = {7 black balls}
Let E, is the event that ball transferred fram the first bag is white and `E_(2)` is the event that the ball transferred from the first bag is black.
AIso, E is the event that the ball drawn from the second bag is white.
`therefore P(E//E_(1))=10/17,P(E//E_(2))=9/17`
and `P(E_(1))=4/9and P(E_(2))=5/9`
`thereforeP(E)=P(E_(1))cdotP(E//E_(1))+P(E_(2))cdotP(E//E_(2))`
`=4/9cdot10/17+5/9cdot9/17`
`=(40+45)/153=5/9`