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
[tex]p(h)=0.15[/tex]
As a consequence, the probability for a person of NOT being hospitalized during one year is
[tex]p(h^{-1})=1-0.15=0.85[/tex]
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:
[tex]p(h^{-1})^4=(0.85)^4=0.52[/tex]
So, the probability that no one in the family of 4 will be hospitalized during a year is 0.52.
Learn more about probability:
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Probability (None of 4 people get hospitalised) = 0.522
Important Information : Probability (A person being hospitalised) = 0.15
So, Probability (A person not being hospitalised) = 1 - A person being hospitalised = 1 - 0.15 = 0.85
Probability that 4 people are not admitted = Pr (Person 1 not admitted) x Pr (Person 2 not admitted) x Pr (Person 3 not admitted) x Pr (Person 4 not admitted)
= 0.85 x 0.85 x 0.85 x 0.85 = 0.522
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