Four out of five doctors prefer Freds Aspirin Thinking about

\"Four out of five doctors prefer Fred\'s Aspirin.\" Thinking about sampling and exhaustive categories, what is wrong with this statement? Can you think of other, similarly misleading statements?

Solution

let a,b,c,d,e be the five doctors.

and A,B,C,D,E be events that a,b,c,d,e prefer fred\'s aspirin respectively.

these events are independent and exhaustive.

now we select a random sample of size four from these five doctors. let the sample contains a,b,d and e. and find that these four prefer the aspirin. so four out of five doctors like the aspirin. but that does not mean that that c does not prefer the aspirin. so based on a sample of sixe of four we can not infer anything.

and in probability sense if one take a huge sample of doctors then the probability of any rondomly chosen doctor to prefer the aspirin is 4/5.