Question

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that

(i) all the three balls are blue balls

(ii) all the balls are of different colours.

Answer 1

Out of 20 balls, three balls can be drawn in ${}^{20}{C}_3$ ways.

$\therefore$ Total number of elementary ways = ${}^{20}{C}_3$

(i) Let E be the event that all the three balls are blue

$\therefore n\left(E\right){=}^9{C}_3$

$\therefore P\left(E\right)=\frac{{}^9{C}_3}{{}^{20}{C}_3}$

$=\frac{9\times 8\times 7}{20\times 19\times 18}=\frac{7}{95}$

(ii) Let E be the event that all the balls are of different colour

$\therefore n\left(E\right){=}^8{C}_1{\times }^3{C}_1{\times }^9{C}_1$

$\therefore P\left(E\right)=\frac{{}^8{C}_1{\times }^3{C}_1{\times }^9{C}_1}{{}^{20}{C}_3}=\frac{8\times 3\times 9}{{}^{20}{C}_3}=\frac{18}{95}$