Question

A man and his wife appear for an interview for two posts. The probability of the husband’s selection is $\frac { 1 } { 7 }$ and that of wife’s selection is $\frac { 1 } { 5 }$. What is the probability that only one of them will be selected.

• A. $\frac { 1 } { 7 }$
• B. $\frac { 2 } { 7 }$
• C. $\frac { 3 } { 7 }$
• D. None of these

Answer 1

Answer: (B)

$\frac { 2 } { 7 }$

Answer 2

The probability of husband is not selected $= 1 - \frac { 1 } { 7 } = \frac { 6 } { 7 }$ ;

The probability that wife is not selected $= 1 - \frac { 1 } { 5 } = \frac { 4 } { 5 }$

The probability that only husband is selected $= \frac { 1 } { 7 } \times \frac { 4 } { 5 } = \frac { 4 } { 35 }$ ;

The probability that only wife is selected $= \frac { 1 } { 5 } \times \frac { 6 } { 7 } = \frac { 6 } { 35 }$

Hence, required probability$= \frac { 6 } { 35 } + \frac { 4 } { 35 } = \frac { 10 } { 35 } = \frac { 2 } { 7 }$.