Question: Ten million people enter a certain lottery. For each person, the chance of winning is one in ten million, independently.
(a) Find a simple, good approximation for the PMF of the number of people who win the lottery.
(b) Congratulations! You won the lottery. However, there may be other winners. Assume now that the number of winners other than you is W ˜ Pois(1), and that if there is more than one winner, then the prize is awarded to one randomly chosen winner. Given this information, find the probability that you win the prize (simplify).