# Math Help - Applications of Probability

1. ## Applications of Probability

The probability that someone will be hospitalized some time during the next year is 0.07. If you consider 4 people who are unknown to eachother, find the probability that:

a.) 1 of them will be hospitalized during the next year

b.) none of them will be hospitalized during the next year

c.) 3 of them will be hospitalized during the next year

What I have so far.

a.) 0.07 / 4 = 0.0175

0.0175 that one will be hospitalized

b.) would it not just be 0.07?

Any help is GREATLY appreciated. Thanks!!

2. 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 = $4 \times 0.93^3 \times 0.07$

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