Is this independent or conditional probability?

Question

2000 people are polled about the flu vaccine. Of those who had received the vaccine, 72 contracted the flu. Of those who did not receive the vaccine, 320 contracted the flu. Of the 2000 phone calls made, 720 had received the vaccine.

Thanks for the help

2000 people are polled about the flu vaccine. Of those who had received the vaccine, 72 contracted the flu. Of those who did not receive the vaccine, 320 contracted the flu. Of the 2000 phone calls made, 720 had received the vaccine.

I know how to do all the math involved, but one question question asks: What type of probability is this example problem? How do you know?

Sorry if i did not make this more clear earlier!

Answer 1

I'm not quite sure what you are asking. Maybe whether or not getting the flu and having the vaccine are independent?

P(Vaccine) = 720/2000 = 0.36 (actually not important here)
P(Flu | Vaccine) = 72/720 = 0.1
P(Flu | No vaccine) = 320/(2000-720) = 0.25.

So, no, getting the flu and having had the vaccine are dependent. The probability of getting the flu changes with whether or not you took the vaccine.

Note that with the probabilities that I have up there, P(Flu | Vaccine) = 72/720 since we are only looking at the vaccine people who got the flu.

P(Flu | No vaccine) = 320/1280 because here we are only at the non-vaccine people who got the flu.

edit: Um, well, I guess this is an example of conditional probabilities. I can't really think of what else it could be. That question is not very clear to me, so that's probably why you're having problems.

Answer 2

Of those who received vaccine =
p ( caught flu conditional on had vaccine) = 72 / 2000
similarly
p( caught flu conditional on NOT had vaccine ) =320 / 2000

p ( had vaccine ) = 720 / 2000 is not conditional

Please note I have used observed x / population as a proxy for probability of x .. this is commonplace and intuitive but there are philosophical objections.

Answer 3

Well, you can certainly use conditional probability here. For example:

Prob[person got flu | person got vaccine] =
Prob[person got flu and vaccine] / Prob[person got vaccine] =
72/720 = 1/10

and

Prob[person got flu | person did not get vaccine] =
Prob[person got flu and without vaccine] / Prob[person did not get vaccine] =
320/1280 = 1/4

Answer 4

It's independant probability, because the people who recieved the vaccine are different than the people who didn't.

Answer 5

the facts are insufficient i think