Question

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

Answer 1

Let S be the sample space

A be the event of taking 3 red balls and B be the event of taking one red and
2 black balls.

A bag contains 7 red balls and 3 black balls.

3 balls are drawn at random.

∴ The number of outcomes n(S) = 11C₃ 

= `(11 xx 10 xx 9)/(1 xx 2 xx 3)`

= 11 × 5 × 3

= 165

n(A) = 7C₃ 

= `(7 xx 6 xx 5)/(1 xx 2 xx 3)`

= 35

n(B) = 7C₁ × 4C₂ 

= `7 xx (4 xx 3)/(1 xx 2)`

= 7 × 6

= 42

P(getting 3 red balls) = P(A)

= `("n"("A"))/("n"("S"))`

= `35/165`

= `7/33`