1/3 points | Previcus A Consider a lottery game in which you purchase tickets wi

Question

1/3 points | Previcus A 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 o.01? ty N 1000 10000 50000 5000 (b) Suppase the lattery game is offered in 200 cities across the U.S. every yea fo 10 years. Suppase there are 1000 peuple in eath ity who purchase 100 tikets every ir i. Suppose you are one of the 200000 repeat players. At the end ot the 10-year period, what is the probbility that you will have won the lottery at least once? i. 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? the lltery is offered

Explanation / Answer

b) ( i )

Note that the probability of winning a lottery in any year is 100/1000000 = 1/10000=0.0001 = p

n = number of years ( trials ) = 10

Let X = number of lottery win by one of the specified person.

So here we want to find P ( X >= 1 ) = 1 - p( X = 0) .......( 1 )

Let P( X = 0) = P( he is not win a lottery in 10 years) = (1 - p)^10 = 0.9999^10 = 0.999

Plug this value inb equation ( 1 ) , we get

P ( X >= 1 ) = 1 - p( X = 0) = 1 - 0.999 = 0.001

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