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

Question

Based on data from a statistical abstract, only about 20% of senior citizens (65 years old or older) get the flu each year. However, about 22% of the people under 65 years old get the flu each year. In the general population, there are 10.5% 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 flu this season?


(b) What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?

(c) Repeat parts (a) and (b) for a community that has 95% senior citizens.

(d) Repeat parts (a) and (b) for a community that has 54% senior citizens.

Explanation / Answer

Let

S = senior citizen
F = gets flu

a)

P(F n S) = P(S) P(F|S) = 0.105*0.20 = 0.021 [ANSWER]

*************

b)

P(F n S') = P(S') P(F|S') = (1-0.105)*(0.22) = 0.1969 [ANSWER]

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c)

a)

P(F n S) = P(S) P(F|S) = 0.95*0.20 = 0.19 [ANSWER]

*************

b)

P(F n S') = P(S') P(F|S') = (1-0.95)*(0.22) = 0.011 [ANSWER]

****************************************************

d)

a)

P(F n S) = P(S) P(F|S) = 0.54*0.20 = 0.108 [ANSWER]

*************

b)

P(F n S') = P(S') P(F|S') = (1-0.54)*(0.22) = 0.1012 [ANSWER]

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