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प्रश्न
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that one is black and two are red.
उत्तर
3 balls can be drawn from 11 balls in 11C3
= `(11 × 10 × 9)/(1 × 2 × 3)`
= 11 × 15 ways
∴ n(S) = 11 × 15
Let B ≡ the event that one is black and two are red One black ball can be drawn from 7 black balls in 7C1 ways and 2 red balls can be drawn from 4 red balls in 4C2 ways.
∴ n(B) = 7C1 × 4C2 = 7 × 6
∴ n(B) = 7 × 6
∴ P(B) = `("n"("B"))/("n"("S"))`
= `(7 xx 6)/(11 xx 15)`
= `14/55`.
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