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Question
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.
Solution
Possible selections are as follows:
1 red ball from bag-I, 2 red balls from bag-II
or 1 white ball from bag-I, 2 white balls from bag-II
∴ Probability of drawing three balls of the same colour
i.e., P(E) = `(""^3"C"_1)/(""^7"C"_1) xx (""^2"C"_2)/(""^5"C"_2) + (""^4"C"_1)/(""^7"C"_1) xx (""^3"C"_2)/(""^5"C"_2)`
= `3/7 xx 1/10 + 4/7 xx 3/10`
= `3/70 + 12/70`
= `15/70`
∴ P(E) = `3/14`
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