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 24% of the people under 65 years old get the flu each year. In the general population, there are 13.5% 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? Incorrect: Your answer is incorrect. (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? Incorrect: Your answer is incorrect. (c) Repeat parts (a) and (b) for a community that has 85% senior citizens. (a) (b) (d) Repeat parts (a) and (b) for a community that has 45% senior citizens. (a) (b)

Answer 1

a) There is a 1.76% probability that a person selected at random from the general population is senior citizen who will get the flu this season.

b) There is a 20.76% 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 - a)

There is a 11.05% probability that a person selected at random from the general population is senior citizen who will get the flu this season.

c - b)

There is a 3.6% probability that a person selected at random from the general population is a person under age 65 who will get the flu this year.

d - a)

There is a 5.85% probability that a person selected at random from the general population is senior citizen who will get the flu this season.

d - b)

There is a 13.2% probability that a person selected at random from the general population is a person under age 65 who will get the flu this year.

Explanation:

We have these following percentages:

13.5% of senior citizens

13% of the senior citizens get the flu

100 - 13.5 = 86.5% of people under 65 years old get the flu.

24% of people under 65 year old get the flu.

(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?

13.5% of the population are senior citizens. Of those, 13% get the flu. So

`P = 0.135(0.13) = 0.0176`

There is a 1.76% 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?

86.5% of the population are under 65 years old. Of those, 24% will get the flu. So:

`P = 0.865(0.24) = 0.2076`

There is a 20.76% 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 85% senior citizens.

Now, 85% of the population are senior citizens and 100-85 = 15% are under 65 years old.

a) 13% of the senior citizens get the flu. So:

`P = 0.85(0.13) = 0.1105`

There is a 11.05% probability that a person selected at random from the general population is senior citizen who will get the flu this season.

b) 24% of non-senior citizens get the flu. So:

`P = 0.15(0.24) = 0.036`

There is a 3.6% probability that a person selected at random from the general population is a person under age 65 who will get the flu this year.

d) Repeat parts (a) and (b) for a community that has 45% senior citizens.

Now, 85% of the population are senior citizens and 100-45 = 55% are under 65 years old.

a) 13% of the senior citizens get the flu. So:

`P = 0.45(0.13) = 0.0585`

There is a 5.85% probability that a person selected at random from the general population is senior citizen who will get the flu this season.

b) 24% of non-senior citizens get the flu. So:

`P = 0.55(0.24) = 0.132`

There is a 13.2% probability that a person selected at random from the general population is a person under age 65 who will get the flu this year.