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Question
Bag I contains 3 black and 2 white balls, Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.
Solution
Given that bag I = {3B, 2W}
And bag II = {2B, 4W}
Let E1 = The event that bag I is selected
E2 = The event that bag II is selected
And = The event that a black ball is selected
∴ P(E1) = `1/2`
P(E2) = `1/2`
`"P"("E"/"E"_1) = 3/5`
And `"P"("E"/"E"_2) = 1/3`
P(E) = `"P"("E"_1)."P"("E"/"E"_1) + "P"("E"_2)."P"("E"/"E"_2)`
= `1/2 xx 3/5 + 1/2 xx 1/3`
= `3/10 + 1/6`
= `(9 + 5)/30`
= `14/30`
= `7/15`
Hence, the required probability is `7/15`.
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