Question

Based on data from a statistical abstract, only about 10% of senior citizens (65 years old or older) get the flu each year. However, about 27% 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?

(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 92% senior citizens.

(d) Repeat parts (a) and (b) for a community that has 52% senior citizens.

Answer 1

a. .10 * .15 = ?

b. .27 * (1-.15) = ?

Use similar process for c and d.

Answer 2

Idk

Answer 3

[AI-generated answer — Step-by-Step Bot]

To solve this problem, we can use the concept of conditional probability. Let's break down the steps for each part:

(a) To find the probability that a random person from the general population is a senior citizen who will get the flu this season, we need to find the intersection of these two events: being a senior citizen and getting the flu.

Let's denote:
A = being a senior citizen
B = getting the flu

From the given information:
P(A) = 0.15 (probability of being a senior citizen)
P(B|A) = 0.10 (probability of getting the flu given that the person is a senior citizen)

To find P(A ∩ B), we can multiply the probabilities:
P(A ∩ B) = P(A) * P(B|A)

Substituting the values:
P(A ∩ B) = 0.15 * 0.10 = 0.015

Therefore, the probability that a random person from the general population is a senior citizen who will get the flu this season is 0.015.

(b) Similarly, to find the probability that a random person from the general population is a person under age 65 who will get the flu this year, we need to find the intersection of these two events: being under age 65 and getting the flu.

Let's denote:
C = being under age 65
D = getting the flu

From the given information:
P(C) = 1 - P(A) = 1 - 0.15 (probability of being under age 65)
P(D|C) = 0.27 (probability of getting the flu given that the person is under age 65)

To find P(C ∩ D), we can multiply the probabilities:
P(C ∩ D) = P(C) * P(D|C)

Substituting the values:
P(C ∩ D) = (1 - 0.15) * 0.27 = 0.85 * 0.27 = 0.2295

Therefore, the probability that a random person from the general population is a person under age 65 who will get the flu this year is 0.2295.

(c) Let's repeat the calculations for a community that has 92% senior citizens.

For part (a):
P(A) = 0.92
P(B|A) = 0.10

P(A ∩ B) = P(A) * P(B|A) = 0.92 * 0.10 = 0.092

Therefore, the probability in this community is 0.092.

For part (b):
P(C) = 1 - P(A) = 1 - 0.92 = 0.08
P(D|C) = 0.27

P(C ∩ D) = P(C) * P(D|C) = 0.08 * 0.27 = 0.0216

Therefore, the probability in this community is 0.0216.

(d) Let's repeat the calculations for a community that has 52% senior citizens.

For part (a):
P(A) = 0.52
P(B|A) = 0.10

P(A ∩ B) = P(A) * P(B|A) = 0.52 * 0.10 = 0.052

Therefore, the probability in this community is 0.052.

For part (b):
P(C) = 1 - P(A) = 1 - 0.52 = 0.48
P(D|C) = 0.27

P(C ∩ D) = P(C) * P(D|C) = 0.48 * 0.27 = 0.1296

Therefore, the probability in this community is 0.1296.

Answer 4

[AI-generated answer — Explain Bot]

To find the probabilities, we need to use the given information and apply some basic statistics concepts.

(a) Let's 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 know that only 10% of senior citizens get the flu. The general population has a 15% of senior citizens. First, we need to calculate the probability that a randomly chosen person from the general population is a senior citizen:

P(Senior Citizen) = 15% = 0.15

Once we know the person is a senior citizen, the probability of getting the flu is 10%:

P(Flu | Senior Citizen) = 10% = 0.10

To find the probability that a person is both a senior citizen and will get the flu, we multiply the two probabilities:

P(Senior Citizen and Flu) = P(Senior Citizen) * P(Flu | Senior Citizen)
= 0.15 * 0.10
= 0.015

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 0.015 (or 1.5%).

(b) Now let's 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 know that 27% of people under 65 years old get the flu.
We already calculated the probability that a person is a senior citizen (P(Senior Citizen) = 0.15). To find the probability that a person is under 65, we subtract the probability of being a senior citizen from 1:

P(Under 65) = 1 - P(Senior Citizen)
= 1 - 0.15
= 0.85

To find the probability that a person is both under 65 and will get the flu, we multiply the two probabilities:

P(Under 65 and Flu) = P(Under 65) * P(Flu | Under 65)
= 0.85 * 0.27
= 0.2295

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 0.2295 (or 22.95%).

(c) To repeat parts (a) and (b) for a community that has 92% senior citizens, we use the same method, but with different probabilities.

For part (a):
P(Senior Citizen) = 92% = 0.92
P(Flu | Senior Citizen) = 10% = 0.10

P(Senior Citizen and Flu) = P(Senior Citizen) * P(Flu | Senior Citizen)
= 0.92 * 0.10
= 0.092

Therefore, the probability that a person selected at random from a community with 92% senior citizens is a senior citizen who will get the flu this season is 0.092 (or 9.2%).

For part (b):
P(Under 65) = 1 - P(Senior Citizen)
= 1 - 0.92
= 0.08

P(Under 65 and Flu) = P(Under 65) * P(Flu | Under 65)
= 0.08 * 0.27
= 0.0216

Therefore, the probability that a person selected at random from a community with 92% senior citizens is a person under age 65 who will get the flu this year is 0.0216 (or 2.16%).

(d) To repeat parts (a) and (b) for a community that has 52% senior citizens, we use the same method, but with different probabilities.

For part (a):
P(Senior Citizen) = 52% = 0.52
P(Flu | Senior Citizen) = 10% = 0.10

P(Senior Citizen and Flu) = P(Senior Citizen) * P(Flu | Senior Citizen)
= 0.52 * 0.10
= 0.052

Therefore, the probability that a person selected at random from a community with 52% senior citizens is a senior citizen who will get the flu this season is 0.052 (or 5.2%).

For part (b):
P(Under 65) = 1 - P(Senior Citizen)
= 1 - 0.52
= 0.48

P(Under 65 and Flu) = P(Under 65) * P(Flu | Under 65)
= 0.48 * 0.27
= 0.1296

Therefore, the probability that a person selected at random from a community with 52% senior citizens is a person under age 65 who will get the flu this year is 0.1296 (or 12.96%).