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.

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.

Question 1: 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.

Question 2: 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

1) P(winning the lottery at least once) = 1- P(not winning the lottery on all 10 years)

= 1 - (1 - 1/200000)10

= 0.00005

2) P( a particular person winning the lottery multiple times) = 1 - P(winning once) - P(not winning)

= 1 - (10(1/200000) x (1-1/200000)9 ) - (1 - 1/200000)10

= 1.124x10-9

So, probability of at least one of the 200,000 people will have won the lottery multiple time = 200,000 x 1.124x10-9

= 0.000225

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