A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

$ns=C230$

 Let A be the event of getting two oranges and 

 B be the event of getting two non-defective fruits.

 and  $A\cap B$ be the event of getting two non-defective oranges

  $\therefore PA=\frac{C}{2}, PB=\frac{C}{2} and PA\cap B=\frac{C}{2}$

  $\therefore PA\cup B=PA+PB-PA\cap B$

=  $\frac{C}{2}+\frac{C}{2}-\frac{C}{2}=\frac{316}{435}$