Hi Dudley,
The best you can say is that the probability that at least one of them gets the flu is at least 75%.
The mathematical relationship is
Pr(Josh gets the flu or John gets the flu)
= Pr(Josh gets the flu) + Pr(John gets the flu)  Pr(Josh gets the flu and John gets the flu)
= 0.75 + 0.25  Pr(Josh gets the flu and John gets the flu)
From what you sent I have no way to evaluate Pr(Josh gets the flu and John gets the flu). That is I have no idea of the probability that both Josh and John get the flu. The most I can say is that it is between 0% and 25%.
If this is a textbook problem then I expect that the author wants you to assume that the event that Josh gets the flu and the event that John gets the flu are independent. If this is the case then
Pr(Josh gets the flu and John gets the flu) = Pr(Josh gets the flu) Pr(John gets the flu) = 0.75 0.25
Penny
