1.

There are 3 bags, each containing 5 white and 3 black balls. Also, there are 2 bags, each containing 2 white and 4 black balls. A white ball is drawn at random. Find the proqability that this ball is from a bag of the first group.

Answer»

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Solution :Let `E_1` = event of selecting a bag from the first GROUP, and
`E_2` = event of selecting a bag from the SECON group.
Then, `P(E_1)=3/5 and P(E_2)=2/5`
Let E = event that the ball drawn is WHITE. Then,
`P(E//E_1)=5/8,P(E//E_2)=2/6=1/3`.
`:. P(E_1//E)=(P(E//E_1).P(E_1))/(P(E//E_1).P(E_1)+P(E//E_2).P(E_2))`


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