# A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that all are black - Mathematics and Statistics

Sum

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

Concept: Concept of Probability
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