Question

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that

(i) both the balls are red

(ii) one ball is red and the other is black

(iii) one ball is white.

Answer 1

7 white, 5 black and 3 red balls Since two balls are drawn at random

$\therefore n\left(S\right)=\frac{15}{2}$

(i) E be the event that both the balls are red

$\therefore n\left(E\right){=}^3{C}_2$

$\therefore P\left(E\right)=\frac{{}^3{C}_2}{{}^{15}{C}_2}=\frac{3\times 2}{15\times 4}=\frac{1}{35}$

(ii) E be the event that one ball is red and other is black

$\therefore n\left(E\right){=}^3{C}_1{\times }^5{C}_1$

$\therefore P\left(E\right)=\frac{{}^3{C}_1{\times }^5{C}_1}{{}^{15}{c}_2}=\frac{7\times 6\times 2}{14\times 15}=\frac{8}{15}$