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 23% 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?

Answer 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?

(c) Repeat parts (a) and (b) for a community that has 85% senior citizens.

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

Answer 2

@phi

Answer 3

To keep the numbers simple, let's say there are 100 people (and we allow "fractions" of a person )

From
** In the general population, there are 13.5% senior citizens (65 years old or older)***
we divide the population into
86.5 young 13.5 old (note this adds up to 100)

***10% of senior citizens (65 years old or older) get the flu each year. ***
so 10% of 13.5 get the shot: 1.35
and the rest do not get a shot: 90% of 13.5 = .9 * 13.5 = 12.15

*** 23% of the people under 65 years old get the flu each year***
that means 0.23 * 86.5 = 19.9 young get a shot
and .77 *86.5 = 66.6 young do not get a shot

Answer 4

now form a table showing the different categories


young old
shot 19.9 1.35
no shot 66.6 12.15


**** (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?****

probability is "number of outcomes that meet the criteria" divided by total number

the number of people in the old/shot category is 1.35
total number is 100.
so probability is 1.35/100 or 1.35% chance of picking an old person who got a shot.