Based on data rom a statistical abstract, only about 20% o senior citizens 65 ye

Question

Based on data rom a statistical abstract, only about 20% o senior citizens 65 years old or older get the each year. However, about 28% of the people under 65 years old get the flu each yea population, there are 13.5% senior citizens (65 years old or older). (Round your answers to three decimal places.) n the general (a) What is the probability that a person selected at random from the gencral population is senior citizen who will get the flu this scason? (b) What is the probability that a person selected at random frorm 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 89% senior citizens. (d) Repeat parts (a) and (b) for a community that has 46% 5enlor citizens.

Explanation / Answer

Here we are given that:

P( flu | senior ) = 0.2 and P( flu | under 65 ) = 0.28

Also, we are given that P( senior ) = 0.135, therefore P( under 65 ) = 1 - P( senior ) = 1 - 0.135 = 0.865

a) The probability that is required here is:

P( senior and flu )

This is computed using the Bayes theorem as:

P( senior and flu ) = P( flu | senior ) P( senior ) = 0.2*0.135 = 0.027

Therefore 0.027 is the required probability here.

b) The probability that is required here is:

P( under 65 and flu )

This is computed using the Bayes theorem as:

P( under 65 and flu ) = P( flu | under 65 ) P( under 65 ) = 0.28*0.865 = 0.242

Therefore 0.242 is the required probability here.

c) For a community where P( senior ) = 0.89, therefore P( under 65 ) = 1 - 0.89 = 0.11

Here the 2 probabilities are computed as:

P( senior and flu ) = P( flu | senior ) P( senior ) = 0.2*0.89 = 0.178
P( under 65 and flu ) = P( flu | under 65 ) P( under 65 ) = 0.28*0.11 = 0.031

d) For a community where P( senior ) = 0.46, therefore P( under 65 ) = 1 - 0.46 = 0.54

Here the 2 probabilities are computed as:

P( senior and flu ) = P( flu | senior ) P( senior ) = 0.2*0.46 = 0.092
P( under 65 and flu ) = P( flu | under 65 ) P( under 65 ) = 0.28*0.54 = 0.151

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