(i) Given that, 5 mangoes and 4 apples are in the box.
Two fruits out of 9 can be chosen in 9C2 = 36 ways.
One mango and one apple can be chosen in 4C1 × 5C1 = 20 ways
∴ Probability = \(\frac{20}{36} = \frac 59\)
(ii) 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
= \(\frac {9\times 8}{ 1 \times 2}\)
= 9 × 4
= 36
n(A) = 5C2
= \(\frac{5\times 4}{1\times 2}\)
= 10
n(B) = 4C2
= \(\frac{4 \times 3}{1 \times 2}\)
= 6
P(taking 2 fruits are of the same colour)
= P(A or B)
= P(A ∪ B)
= P(A) + P(B)
\(= \frac{n(A)}{n(S)} + \frac{n(B)}{n(S)}\)
\(= \frac{10}{36} + \frac 6{36}\)
\(= \frac{10 + 6}{36}\)
\(= \frac{16 }{36}\)
\(= \frac 49\)