Based on data from a statistical abstract, only about 20% of senior citizen (65

Question

Based on data from a statistical abstract, only about 20% of senior citizen (65 years old or older)get the each year. However, about 30% of the people under 65 years old get the each year. In the genera: population, there are 19% senior citizens (65 years old or older). (a) What is the probability that a person selected at random from the general population is senior citizen who will get the this season? (b) What is the probability that a person selected at random from general population in a person under age 65 who will get the this year? (c) Repeat parts (a) and (b) for a community that has 89% senior citizen. (d) Repeat parts (a) and (b) for a community that has 46% senior citizen.

Explanation / Answer

We will use the definition of conditional probability to solve these problems.

P(A and B) = P(A) *P(B | A)

(a)

P(senior citizen and get flu this season) = P(senior citizen)*P(get flu this season | senior citizen) = 0.10*0.20=0.02

(b)

P(under age 65 and get flu this season) = P(under age 65)*P(get flu this season | under age 65) = (1-0.10)*0.30 = 0.27

(c)

       (a) P(senior citizen and get flu this season) = 0.59*0.20 = 0.118

        (b) P(under age 65 and get flu this season) = (1-0.59)*0.30 = 0.123

(d)

       (a) P(senior citizen and get flu this season) = 0.46*0.20 = 0.092

        (b) P(under age 65 and get flu this season) = (1-0.46)*0.30 = 0.162

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