Rakib and his wife appear in an interview for two vacancies in the same post. The probability of Rakib's selection is (1/7) and the probability of his wife's selection is (1/5). What is the probability that only one of them is selected?

Question: Rakib and his wife appear in an interview for two vacancies in the same post. The probability of Rakib's selection is (1/7) and the probability of his wife's selection is (1/5). What is the probability that only one of them is selected?

Solution:
the probability of Rakib's selection is (1/7)
the probability of Rakib's not selection is = 1 - (1/7)
= (7 - 1)/7
= 6/7

the probability of his wife's selection is (1/5)
the probability of his wife's not selection is = 1 - (1/5)
= (5 - 1)/5
= 4/5

the probability that only one of them is selected is = (1/7) × (4/5) + (1/5) (6/7)
= (4/35) + (6/35)
= (6 + 4)/35
= 10/35
= 2/7