One hundredllion people enter a certain lottery. For each person, the chance of

Question

One hundredllion people enter a certain lottery. For each person, the chance of winning is one in one hundred million, independently. (a) What can be used to approximate the PMF of the number of people who win the lottery? b) Suppose you won the lottery. However, there may be other winners. Assume that the i. If the total price (1 million dollars) needs to be divided equally among all winners, ii. If the total price (1 million dollars) is awarded to one of the W+1 winners randomly number of winners other than you is W Poisson(1) find your expected reward And each winner has equal probability to be awarded. What is the probability that you win the prize?

Explanation / Answer

a) In this case poisson distribution is applicable

since in poisson distribution probability of success is very small

given P = [1 / one hundred million] is very small chance

b)

i) Expected reward = 100 million persons / 1 million dollors = 100 dollars for each person

ii) P = 1 million dollars /101 million persons = 0.0099

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