Question

If the probability of being hospitalized during a year is 0.1, find the probability that no one in a family of six will be hospitalized in a year.

a) 0.531441
b) 0.729
c) 0.9
d) 0.3487

Answer 1

The probability that no one in a family of six will be hospitalized in a year, given the individual probability of 0.1, is calculated as the complement to the sixth power, resulting in a probability of 0.531441.

Step-by-step explanation:

If the probability of being hospitalized during a year is 0.1, the probability that no one will be hospitalized in a family of six during a year can be found by taking the complement of the probability of being hospitalized for each individual, and then raising this to the power of six, since each family member is assumed to have an independent risk.

Let's take the complement of the probability of one person being hospitalized, which is 1 - 0.1 = 0.9. Then, for six independent chances, we raise this probability to the sixth power:

(0.9)6 = 0.531441

Therefore, the probability that no one in a family of six will be hospitalized in a year is 0.531441.