Question

Two balls are drawn at random with replacement from a box containing 10 black aid 8 red balls. Find the probability that 

(a) Both the balls are red.

(b) One of them is black and the other is red

Answer 1

(a) P (both all red) \(=\frac{8}{18} \times \frac{8}{18}=\frac{16}{81}\)

(b) P (one of them is black and other red) = P(First ball black, second red) or P (First red, second black) 

\(=\frac{10}{18} \times \frac{8}{18}+\frac{8}{18} \times \frac{10}{18}=\frac{20}{81}+\frac{20}{81}=\frac{40}{81}\)