Consider a lottery game in which you purchase tickets with random numbers on the

Question

Consider a lottery game in which you purchase tickets with random numbers on them, and suppose the probability any one ticket is a winner is one in a million.

(a) What is the approximate minimum number of tickets you should buy if you want the probability of getting at least one winner to be 0.01?

(b) Suppose the lottery game is offered in 200 cities across the U.S. every year for 10 years. Suppose there are 1000 people in each city who purchase 100 tickets every time the lottery is offered. Suppose you are one of the 200000 repeat players. At the end of the 10-year period, what is the probability that you will have won the lottery at least once? Answer to 1 significant figure.

(c) At the end of the 10-year period, what is the probability that at least one of the 200000 people will have won the lottery multiple times? Answer to 1 significant figure.

Explanation / Answer

A) suppose u purchase n lotteries

P(winning) = 0.01

So, n x 1/1,000,000 = 0.01

Number of lotteries to be purchased = 10,000

B)P(you winning at least once in 10 years) = 10/number of players

10/(200,000) = 0.00005

(Probability of winning more than once is negligibly small)

C) P(winning mutiple times) = 1 - P(not winning in 10 years) - P(winning once in 10 years)

=1 - (199,999/200,000)10 - 10x1/200,000x(199,999/200,000)9

= 1..1x10-9

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