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

= ${\displaystyle \frac{9\times 8}{1\times 2}}$

= 9 × 4

= 36

n(A) = 5C₂

= ${\displaystyle \frac{5\times 4}{1\times 2}}$

= 10

n(B) = 4C₂

= ${\displaystyle \frac{4\times 3}{1\times 2}}$

= 6

P(taking 2 fruits are of the same colour)

= P(A or B)

= P(A ∪ B)

= P(A) + P(B)

= ${\displaystyle \frac{\text{n}\left(\text{A}\right)}{\text{n}\left(\text{S}\right)}+\frac{\text{n}\left(\text{B}\right)}{\text{n}\left(\text{S}\right)}}$

= ${\displaystyle \frac{10}{36}+\frac{6}{36}}$

= ${\displaystyle \frac{10+6}{36}}$

= ${\displaystyle \frac{16}{36}}$

= ${\displaystyle \frac{4}{9}}$