Find the probability

Question

If the probability of being hospitalized during a certain year is 0.21, find the probability that no one in a family of three will be hospitalized that year.

The probability is  . (Round your answer to five decimal places.)

Answer 1

So the probability, for each person, of being hospitalized that year is 0.21 or 21/100. Let's call that P. That means that the probability of NOT being hospitalized in a year is 1-P, or 0.79 or 79/100. Let's call that Q.

Now let's find the probability that no one in the family is hospitalized. To find the probability that two (or more) independent events both happen, you multiple the probabilities of those two (or more) events together. So the probability a single person IS NOT hospitalized in a year is Q, and this is true for each member of family. So we multiply the probabilities for each person together: Q x Q x Q = 0.49304. And that's our answer!