Question

Pia, Sia and Dia displayed their paintings in an art exhibition. The three artists displayed 15, 5 and 10 of their paintings respectively. A person bought three paintings from the exhibition.

1. Find the probability that he bought one painting from each of them.   [2]
2. Find the probability that he bought all the three paintings from the same person.   [2]

Answer 1

Total number of paintings

= 15 + 5 + 10

= 30

i. Probability of buying one painting from each of them

= `(""^15C_1 xx ""^10C_1 xx ""^5C_1)/(""^30C_3)`

= `(15 xx 10 xx 5)/((30 xx 29 xx 28)/(3 xx 2))`

= `75/406`

ii. Probability of buying three painting from the same person

= `(""^15C_3 + ""^5C_3 + ""^10C_3)/(""^30C_3)`

= `(455 + 10 + 120)/4060`

= `585/4060`

= `117/812`