I look through this question and hardly figure out how to do. The solution seem to be doesnt make sense to me. I dont think anyone will predict it will be done that way. Any comment???
As part of the underwritting process for insurance, each prospective policyholder is tested for high blood pressure. Let X represent the number of tests completed when the first person with high blood pressure is found. The expected value X is 12.5. Calculate the probability that the sixth person tested is the first one with high blood pressure.
The solution goes like this...
we assume that each test for high blood pressure is a bernoulli trial with probability of success p. Then X has the geometric dist. and 12.5=E(x)=1/p.
Therefore p=0.08. using this, we find
p(first 5 do not have high blood pressure)*p(the 6th does have high blood pressure)=(1-0.08)^5.0.08=0.053.