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

$MF#%= \text{P(}\bar{\text{A}}\cap\bar{\text{B}}\text{)}$MF#%(∵ Reference : )

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

$MF#%= \left(1 - \dfrac{1}{3}\right)\left(1 - \dfrac{1}{5}\right)$MF#%

$MF#%= \dfrac{2}{3} × \dfrac{4}{5} = \dfrac{8}{15}$MF#%