Question

A bag contains 8 apple and 6 orange. Four fruits are drawn out one by one and not replaced. What is the probability that they are alternatively of different fruits?

Answer 1

There can be two ways of drawing fruit ,AOAO and OAOA

Probablity of first way (AOAO) = $\frac{8}{14}\times$ $\frac{6}{13}\times$ $\frac{7}{12}\times$ $\frac{5}{11}=\frac{10}{143}$

Probablity of second way (OAOA) = $\frac{6}{14}\times$ $\frac{8}{13}\times$ $\frac{5}{12}\times$ $\frac{7}{11}=\frac{10}{143}$

So,Total probablity = $\frac{20}{143}$