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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 white ball is 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 F be the event that a white ball is selected
∴ P(F) = 1 – P(E) ......[P(E) + P(F) = 1]
= `1 - 7/18`
= `11/18`
Hence, the required probabilities are `7/18` and `11/18`.
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