Answer : Option C

Explanation :

Let A = Event that A gets a job and B = Event that B gets a job
Given that P(A) = 1/5 and P(B) = 1/7
Probability that only one of them gets a job

$MF#%= \text{P}\left[\left(A \cap \bar{\text{B}}\right)\cup \left(\text{B} \cap \bar{\text{A}}\right)\right]$MF#%(∵ Reference : )

$MF#%= \text{P(A)}\left[1 - \text{P(B)}\right] + \text{P(B)}\left[1 - \text{P(A)}\right]$MF#%

$MF#%= \dfrac{1}{5}\left(1 - \dfrac{1}{7}\right) + \dfrac{1}{7}\left(1 - \dfrac{1}{5}\right) = \dfrac{1}{5} \times \dfrac{6}{7} + \dfrac{1}{7}\times \dfrac{4}{5} = \dfrac{6}{35} + \dfrac{4}{35} = \dfrac{10}{35} = \dfrac{2}{7}$MF#%