Question

Kamal and Vimal appeared for an interview for two vacancies. The probability of Kamal’s selection is 1/3 and that of Vimal’s selection is 1/5. Find the probability that only one of them will be selected.

Answer 1

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.