Suppose 15% of senior citizens (people 65 years of age and older) get the flu ea

Question

Suppose 15% of senior citizens (people 65 years of age and older) get the flu each year and 24% of people under 65 years old get the flu each year. Also suppose that the population consists of 12% senior citizens.

(a) If you choose a random person from the population, what is the probability that she is a senior citizen? What is the probability that the person is under 65 years of age?

(b) What is the probability that a a person gets the flu given that she is a senior citizen?

(c) What is the probability that a randomly selected person is both a senior citizen and gets the flu?

(d) What is the probability that person selected at random is a person under age 65 who will get the flu?

Explanation / Answer

Solution:

Lets say
S : senior citizen
F : gets flu
a) P(S) = (0.12), P(S') = (1-0.12) = 0.88
b) P(F|S) = 0.15
c) P(FS) = P(S) P(F|S) = 0.12 * 0.15 = 0.018
d) P(F S') = P(S') P(F|S') = (1-0.12)*(0.24) = 0.2112

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