At the local stadium, there are 60,000 fans attending a football game. It is well known that only a few people at the game will be impartial (i.e., will not care about the outcome of the game). Suppose that each person at the game has probability 1 / 10,000 of being impartial (and that the impartiality of a fan has no bearing on the other fans).
a. Give an exact formula for the probability that 8 of the people at the game are impartial. You do not have to evaluate the formula on your calculator.
b. Use a Poisson estimation for the probability above.
c. Use your calculator to evaluate the Poisson expression that you gave in part b.