Answer :
Answer: The required probability is 2.24%.
Step-by-step explanation:
Since we have given that
Percentage of people are senior citizens ( 65 years old or older ) = 14%
Percentage of people are under 65 years old = 100-14 = 86%
Probability that senior citizens get the flu each year = 16%
Probability that under 65 years old get the flu each year = 30%
So, Probability that a person selected at random from the general population is senior citizen who get the flu this season is given by
[tex]P(S\cap F)={P(F|S)\times P(S)\\\\P(S\cap F)=0.16\times 0.14\\\\P(S\cap F)=0.0224\\\\P(S\cap F)=2.24\%[/tex]Hence, the required probability is 2.24%.
Answer:
Probability that a person selected at random from the general population is senior citizen who will get the flu this season = 0.0224 .
Step-by-step explanation:
We are given that in the general population, there are 14% senior citizens (65 years old or older).
Let Probability of senior citizens (65 years old or older) in the population, P(S) = 0.14
Probability of citizens under 65 years old in the population, P(NS) = 1 - 0.14 = 0.86
Now, let event F = citizens getting flu each year
Probability of senior citizens (65 years old or older) getting flu each year, P(F/S) = 0.16
Probability of citizens under 65 years getting flu each year, P(F/NS) = 0.30
So, probability that a person selected at random from the general population is senior citizen who will get the flu this season = Probability that person is senior citizen(65 years old or older) * Probability of senior citizens (65 years old or older) getting flu each year
= P(S) * P(F/S) = 0.14 * 0.16 = 0.0224.