A brother and sister appear for an interview against two vacant posts in an office. The probability of the brother’s selection is 1/5th and that of the sister’s selections is 1/3rd. What is the probability that one of them is selected ?

A. 1/5

B. 2/5

C. 1/3

D. 2/3

Answer : B. 2/5

Explanation:

Probability that only one of them is selected = (prob. that brother is selected) × (prob. that sister is not selected) + (Prob. that brother is not selected) × (Prob. that sister is selected)

Hence, Required Probability = 1/5 x 2/3 + 4/5 x 1/3
= 2/15 + 4/15
= 6/15
= 2/5.

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