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Question
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that all are black
Solution
The bag contains 7 black and 4 red balls,
i.e., 7 + 4 = 11 balls.
∴ 3 balls can be drawn out of 11 balls in 11C3 ways.
∴ n(S) = 11C3
Let event A: All 3 balls drawn are black.
There are 7 black balls.
∴ 3 black balls can be drawn from 7 black balls in 7C3 ways.
∴ n(A) = 7C3
∴ P(A) = `("n"("A"))/("n"("S"))`
= `(""^7"C"_3)/(""^11"C"_3)`
= `(7 xx 6 xx 5)/(11 xx 10 xx 9)`
= `7/33`
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