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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?
Solution
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`
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