During the holiday rush, there are 100,000 shoppers in a certain region. Each of these shoppers is extremely likely to make a purchase. Suppose that a person makes a purchase with probability 49,999/50,000 and declines to make a purchase with probability 1/50,000. Let X be the number of people who decline to make a purchase.
a. Give an exact formula for the probability that P(X < 3). 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.