A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. One bag is chosen at random. From the selected bag, one ball is drawn. find the probability that the ball drawn is white.

Explanation

Bag I ={3B,2W],Bag II={2B,4W}
Let `E_(1)`=Event that bag I is selected
`E_(2)`=Event that bag II is selected
and E=Event that a black ball is selected
`rArrP(E_(1))=1//2,P(E_(2))=1/2,P(E//E_(1))=3/5,P(E//E_(2))=2/6=1/3`
`thereforeP(E)=P(E_(1))cdotP(E//E_(1))+P(E_(2))cdotP(E//E_(2))`
`1/2cdot3/5+1/2cdot2/6=3/10+2/12`
`=(18+10)/60=28/60=7/15`