Question

Five mangoes and 4 apples are in a box. If two fruits are chosen at random, find the probability that both are of the same variety

Answer 1

Let S be the sample space, A be the event of taking 2 mangoes and B be the event of taking 2 apples

∴ n(s) = 9C₂

= `(9 xx 8)/(1 xx 2)`

= 9 × 4

= 36

n(A) = 5C₂

= `(5 xx 4)/(1 xx 2)`

= 10

n(B) = 4C₂

= `(4 xx 3)/(1 xx 2)`

= 6

P(taking 2 fruits are of the same colour)

= P(A or B)

= P(A ∪ B)

= P(A) + P(B)

= `("n"("A"))/("n"("S")) + ("n"("B"))/("n"("S"))`

= `10/36 + 6/36`

= `(10 + 6)/36`

= `16/36`

= `4/9`