Question

A bag contains three of black ball, four green balls and five red balls. Three balls are drawn

from the bag without replacement. Use a tree diagram to find the probability that the balls

are all of different colours.

Answer 1

Solution:

The probability that the balls are all of different colours

$=P(WGR)+P(WRG)+P(GWR)+P(GRW)+P(RWG)+P(RGW) \\=\dfrac{3}{12} \times \dfrac{4}{11}\times \dfrac{5}{10} + \dfrac{3}{12} \times \dfrac{5}{11}\times \dfrac{4}{10} + \dfrac{4}{12} \times \dfrac{3}{11}\times \dfrac{5}{10} + \dfrac{4}{10} \times \dfrac{5}{11}\times \dfrac{3}{10} + \dfrac{5}{12} \times \dfrac{3}{11}\times \dfrac{4}{10} + \dfrac{5}{12} \times \dfrac{4}{11}\times \dfrac{3}{10}$

$=\dfrac{60}{1320}\times 6 \\=\dfrac3{11}$