Consider A as the event ‘Kamal is selected’ and B as the event ‘Vimal is selected’
So P (A) = 1/3 and P (B) = 1/5
Here
P (only one of them is selected) = P (A and not B or B and not A)
It can be written as
= P (A and not B) + (B and not A)
Substituting the values
= 1/3 [1 – 1/5] + 1/5 [1 – 1/3]
On further calculation
= 4/15 + 2/15
= 2/5
Hence, the probability that only one of them will be selected is 2/5.
