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.

Answer 1

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`.