Question

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

Answer 1

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`