Question

Three bags contain a number of red and white balls as follows:
Bag 1:3 red balls, Bag 2:2 red balls and 1 white ball
Bag 3:3 white balls.
The probability that bag i will be chosen and a ball is selected from it is `"i"/6`, i = 1, 2, 3. What is the probability that a red ball will be selected?

Answer 1

Given that,

Bag I: 3 red balls and no white ball

Bag II: 2 red balls and 1 white ball

Bag III: no red ball and 3 white balls

Let E₁, E₂ and E₃ be the events of choosing Bag I, Bag II and Bag III respectively and a ball is drawn from it.

∴ P(E₁) = `1/6`

P(E₂) = `2/6`

And P(E₃) = `3/6`

 Let E be the event that red ball is selected

∴ P(E) = `"P"("E"_1) * "P"("E"/"E"_1) + "P"("E"_2) * "P"("E"/"E"_2) + "P"("E"_3) * "P"("E"/"E"_3)`

= `1/6 * 3/3 + 2/6 * 2/3 + 3/6 * 0`

= `3/18 + 4/18`

= `7/18`