Based on data from a statistical abstract, only about 13% of senior citizens (65

Question

Based on data from a statistical abstract, only about 13% of senior citizens (65 years old or older) get the flu each year. However, about 26% of the people under 65 years old get the flu each year. In the general population, there are 10% senior citizens (65 years old or older). (Round your answers to three decimal places.) (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 86% senior citizens. (a) (b) (d) Repeat parts (a) and (b) for a community that has 50% senior citizens. (a) (b)

Explanation / Answer

Probability that a person will be senior citizen, P(C) = 0.1
Probability that a senior citizen get the flu, P(F|C) = 0.13
Probability that a non senior citizen get the flu, P(F|C') = 0.26

(A) Required probability, P(C and F) = P(F|C)*P(C) = 0.13*0.1 = 0.013

(B) Required probability, P(C' and F) = P(F|C')*P(C') = 0.26*0.9 = 0.234

(C)
Probability that a person will be senior citizen, P(C) = 0.86

Required probability, P(C and F) = P(F|C)*P(C) = 0.13*0.86 = 0.1118

Required probability, P(C' and F) = P(F|C')*P(C') = 0.26*0.14 = 0.0364

(D)
Probability that a person will be senior citizen, P(C) = 0.5

Required probability, P(C and F) = P(F|C)*P(C) = 0.13*0.5 = 0.065

Required probability, P(C' and F) = P(F|C')*P(C') = 0.26*0.5 = 0.13

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