Question

If two balls are drawn from a bag containing three red balls and four blue balls, find the probability that:
(a) They are of the same colour.
(b) They are of different colours.

Answer 1

Total number of ways of drawing 2 balls ${=}^7{C}_2$

(a) P(Balls are of same colour)
$=\frac{{}^3{C}_2}{{}^7{C}_2}+\frac{{}^4{C}_2}{{}^7{C}_2}=\frac{{}^3{C}_2{+}^4{C}_2}{{}^7{C}_2}$
$=\frac{\frac{3!}{2!.1!}+\frac{4!}{2!.2!}}{\frac{7!}{2!.5!}}=\frac{3+6}{7\times 3}=\frac{9}{21}=\frac{3}{7}$

(b) P(Balls are of different colour) $=\frac{{}^3{C}_1{\times }^4{C}_1}{{}^7{C}_2}=\frac{\frac{3!}{1!.2!}\times \frac{4!}{1!.3!}}{\frac{7!}{2!.5!}}=\frac{3\times 4}{7\times 3}=\frac{4}{7}$