A basket contains 20 apples and 10 oranges out of which 5 apple and 3 orange are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good?

Explanation

A: both are apples

B: both are good

`P(A)=(.^20C_2)/(.^30C_2)`

`P(B)=(.^22C_2)/(.^30C_2)`

`P(AnnB)=(.^15C_2)/(.^30C_2)`

`P(AuuB)=P(A)+P(B)+P(AnnB)`

`=(.^20C_2)/(.^30C_2)+(.^22C_2)/(.^30C_2)-(.^15C_2)/(.^30C_2)`.