Question

In the US about 15% of the population is 65 years or older. It is estimated that 90% of seniors get a flu shot. It is also estimated that 45% of non-seniors get the flu shot. If a US citizen is selected at random:
A) what is the probability that they are under 65years old?
B)what is the probability they are over 65 and did not get a flu shot?
C) what is the probability that they got a flu shot?

Answer 1

A)\[P(age \ge65)=0.15\]
\[P(age <65)=1.00-0.15=you\ can\ calculate\]

Answer 2

B) I assume that the question should be:
"what is the probability they are 65 or older and did not get a flu shot?"
Let A be the event '65 years or older' and let B be the event 'senior did not get a flu shot'.
Then:
P(A) = 0.15
P(B) = 1.0 - 0.9 = 0.1
\[P(A \cap B)=P(A) \times P(B)=0.15\times0.1=you\ can\ calculate\]

Answer 3

C)
Let C be the event 'senior got a flu shot'.
\[P(C)=0.15\times0.9\]
Let D be the event 'non-senior got a flu shot'.
\[P(D)=0.85\times0.45\]
Let E be the event 'US citizen got a flu shot'.
Events C and D are mutually exclusive, therefore:
\[P(E)=P(C)+P(D)=(0.15\times0.9)+(0.85\times0.45)=you\ can\ calculate\]

Answer 4

Thank you! and yes I can do the simple calcualtions or my calculator can :-)

Answer 5

Cool! :)