Question

If the probability of being hospitalized during a year is 0.15 find the probability that no one in the family of 4 will be hospitalized in a year

Answer 1

The probability that no one in the family of 4 will be hospitalized during a year is 0.52

Step-by-step explanation:

The probability for a person to be hospitalized during one year is

$p(h)=0.15$

As a consequence, the probability for a person of NOT being hospitalized during one year is

$p(h^{-1})=1-0.15=0.85$

If we have 4 people in the family, the probability of each of them of NOT being hospitalized during the year is independent from the probability of the others - therefore, these are independent events. This means that the total probability of the 4 people of not being hospitalized during a year is:

$p(h^{-1})^4=(0.85)^4=0.52$

So, the probability that no one in the family of 4 will be hospitalized during a year is 0.52.

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