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There are two bags,one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up

Monjur Alahi

There are two bags,one of which contains 3 black and 4 white balls while the other contains 4 black and 3 white balls. A die is thrown. If it shows up 1 or 3, a ball is taken from the Ist bag but it shows up any other number, a ball is chosen from the II bag. Find the probability of choosing a black ball.


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Salim Ahmed Kawsar

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Since, Bag I= {3 black, 4 white balls}, Bag II = {4 black, 3 white balls}
Let `E_(1)` be the event that bag is selected and `E_(2)` be the event that bag II is selected.
Let `E_(3)` be the event that black ball is chosen
`therefore P(E_(1))=1/6+1/6=1/3 and P(E_(2))=1-1/3=2/3`
and `P(E_(3)//E_(1))=3/7and P(E_(3)//E_(2))=4/7`
`therefore P(E_(3)=P(E_(1))cdotP(E_(3)//E_(1))+P(E_(2))cdotP(E_(3)//E_(2))`
`=1/3cdot3/7+2/3cdot4/7=11/21`

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