# Question

Consider the lottery described.

(a) Assuming six million tickets are sold and that each player selects his/ her number independent of all others, find the exact probability of fewer than 3 players winning the lottery.

(b) Approximate the probability in part (a) using the Poisson approximation to the binomial distribution.

(c) Approximate the probability in part (a) using the central limit theorem. In this example, which approximation is more accurate?

(a) Assuming six million tickets are sold and that each player selects his/ her number independent of all others, find the exact probability of fewer than 3 players winning the lottery.

(b) Approximate the probability in part (a) using the Poisson approximation to the binomial distribution.

(c) Approximate the probability in part (a) using the central limit theorem. In this example, which approximation is more accurate?

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