Answer : Option C

Explanation :

Let A = the event that John is selected and B = the event that Dani is selected.
Given that P(A) = 1/3 and P(B) = 1/5

We know that $MF#%\bar{\text{A}}$MF#% is the event that A does not occur and $MF#%\bar{\text{B}}$MF#% is the event that B does not occur

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

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

$MF#%= \dfrac{1}{3}\left(1 - \dfrac{1}{5}\right) + \dfrac{1}{5}\left(1 - \dfrac{1}{3}\right) = \dfrac{1}{3} \times \dfrac{4}{5} + \dfrac{1}{5}\times \dfrac{2}{3} = \dfrac{4}{15} + \dfrac{2}{15} = \dfrac{2}{5}$MF#%