Question

Based on data from the Statistical Abstract of the United States, 112th Edition, only about 20% of senior citizens (65 years old or older) get the flu each year. However, about 32% 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).

(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? (Use 3 decimal places.)


(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? (Use 3 decimal places.)


(c) Answer parts (a) and (b) for a community that has 87% senior citizens. (Use 3 decimal places.)

(a)
(b)

(d) Answer parts (a) and (b) for a community that has 48% senior citizens. (Use 3 decimal places.)

(a)
(b)

Answer 1

We will use Bayes theorem.

where A and B are events such that P(B) is not zero.

• P(A|B) is a conditional probability:  the likelihood of event A occurring given that B is true.
• P(B|A) is also a conditional probability: the likelihood of event B occurring given that A is true.
• P(A) and P(B) are the marginal probabilities of observing A and B respectively

(a) The probability that a person selected at random from the general population is senior citizen who will get the flu this season is 0.099.

(b) 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 0.901.

(c) For a community that has 87% senior citizens the required probabilities are:
(a) 0.807  
(b) 0.193  

(d) For a community that has 48% senior citizens the required probabilities are:
(a) 0.366  
(b) 0.634