# 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 - Mathematics and Statistics

Sum

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

#### Solution

3 balls can be drawn from 11 balls in 11C3

= (11xx10xx9)/(1xx2xx3)

= 11 × 15 ways

∴ n(S) = 11 × 5

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 × 4C1 = 7 × 6

∴ n(B) = 7 × 6

∴ P(B) = ("n"("B"))/("n"("S"))

= (7  xx 6)/(11 xx 15)

= 14/55

Concept: Concept of Probability
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