Based on data from a statistical abstract, only about 12% 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 15% 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?
1
(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?
2

(c) Repeat parts (a) and (b) for a community that has 90% senior citizens.
(a)
(b)

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

(a) To find the probability that a person selected at random from the general population is a senior citizen who will get the flu this season, we need to multiply the probability of being a senior citizen by the probability of getting the flu.

Probability of being a senior citizen in the general population = 15% = 0.15
Probability of getting the flu for senior citizens = 12% = 0.12

P(senior citizen getting the flu) = (Probability of being a senior citizen) * (Probability of getting the flu)
= 0.15 * 0.12
= 0.018

Therefore, the probability that a person selected at random from the general population is a senior citizen who will get the flu this season is 0.018.

(b) To find 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, we need to multiply the probability of being under age 65 by the probability of getting the flu.

Probability of being under age 65 in the general population = 85% (100% - 15%) = 0.85
Probability of getting the flu for people under age 65 = 24% = 0.24

P(person under age 65 getting the flu) = (Probability of being under age 65) * (Probability of getting the flu)
= 0.85 * 0.24
= 0.204

Therefore, 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 is 0.204.

(c) For a community with 90% senior citizens:
(a) P(senior citizen getting the flu) = (Probability of being a senior citizen) * (Probability of getting the flu)
= 0.9 * 0.12
= 0.108

(b) P(person under age 65 getting the flu) = (Probability of being under age 65) * (Probability of getting the flu)
= 0.1 * 0.24
= 0.024

(d) For a community with 45% senior citizens:
(a) P(senior citizen getting the flu) = (Probability of being a senior citizen) * (Probability of getting the flu)
= 0.45 * 0.12
= 0.054

(b) P(person under age 65 getting the flu) = (Probability of being under age 65) * (Probability of getting the flu)
= 0.55 * 0.24
= 0.132

To solve this problem, we will first calculate the probability for part (a), which asks for the probability that a person selected randomly from the general population is a senior citizen who will get the flu this season.

Given:
- Only 12% of senior citizens get the flu each year.
- 15% of the general population are senior citizens.

To calculate the probability, we need to multiply the two probabilities together. This is because we are looking for the likelihood that both events (being a senior citizen and getting the flu) occur at the same time.

Probability = (probability of being a senior citizen) * (probability of getting the flu)

Probability = 0.15 * 0.12

Now, let's calculate the result:

Probability = 0.018

Therefore, the probability that a person selected at random from the general population is a senior citizen who will get the flu this season is 0.018.

Moving on to part (b), which asks for the probability that a person selected randomly from the general population is a person under age 65 who will get the flu this year.

Given:
- 24% of the people under 65 years old get the flu each year.
- 85% of the general population are under 65 years old.

Using the same method as before, we multiply the probabilities together:

Probability = (probability of being under 65) * (probability of getting the flu)

Probability = 0.85 * 0.24

Calculating the result:

Probability = 0.204

Therefore, 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 is 0.204.

Now, let's move on to parts (a) and (b) for a community that has 90% senior citizens.

Repeating the calculation from before for part (a), where a community has 90% senior citizens:

Probability = (probability of being a senior citizen) * (probability of getting the flu)

Probability = 0.9 * 0.12

Calculating the result:

Probability = 0.108

Therefore, the probability that a person selected at random from a community with 90% senior citizens is a senior citizen who will get the flu this season is 0.108.

For part (b), where a community has 90% senior citizens:

Probability = (probability of being under 65) * (probability of getting the flu)

Probability = 0.1 * 0.24

Calculating the result:

Probability = 0.024

Therefore, the probability that a person selected at random from a community with 90% senior citizens is a person under age 65 who will get the flu this year is 0.024.

Finally, let's repeat parts (a) and (b) for a community that has 45% senior citizens.

For part (a), where a community has 45% senior citizens:

Probability = (probability of being a senior citizen) * (probability of getting the flu)

Probability = 0.45 * 0.12

Calculating the result:

Probability = 0.054

Therefore, the probability that a person selected at random from a community with 45% senior citizens is a senior citizen who will get the flu this season is 0.054.

For part (b), where a community has 45% senior citizens:

Probability = (probability of being under 65) * (probability of getting the flu)

Probability = 0.55 * 0.24

Calculating the result:

Probability = 0.132

Therefore, the probability that a person selected at random from a community with 45% senior citizens is a person under age 65 who will get the flu this year is 0.132.

a. The probability of being a senior citizen = .15. The probability of a senior citizen getting the flu = .12.

The probability of both/all events occurring is found by multiplying the individual probabilities.

Use the same process for the remaining problems.

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