For (a) I would suggest trying to draw a probability tree but I can see that will get messy and complicated fast.

Think about it like this:

P(1st person goes to hospital) = 0.07 x 0.93 x 0.93 x 0.93

P(2nd person goes to hospital) = 0.93 x 0.07 x 0.93 x 0.93

P(3rd person goes to hospital) = 0.93 x 0.93 x 0.07 x 0.93

P(4th person goes to hospital) = 0.93 x 0.93 x 0.93 x 0.07

So to find the answer add the probabilities =

Oh and for (b), the chance of one person not being hospitalised is 0.93. So the chance of the 4 people not being hospitalised is 0.93 x 0.93 x 0.93 x 0.93