Question

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

Answer 1

Let A denotes Apples and O denotes Oranges and it is given that there are 20 apples and 10 oranges. Out of 20 apples 5 and 10 oranges 3 are defective. `P(AUB)=P(A)+P(B)-P(AnnB)` `n(A)=(20C_2)` `P(A)=(20C_2)/(30C_2)` `n(B)=22C_2` `P(B)=(22C_2)/(30C_2)` `n(AnnB)=15C_2` `P(AnnB)=(15C_2)/(30C_2)` `P(AUB)= (20C_2)/(30C_2)+(22C_2)/(30C_2)-(15C_2)/(30C_2)` `P(AUB)=0.72`