Consider a simplified lottery game in which each ticket you purchase gives you o
ID: 3203264 • Letter: C
Question
Consider a simplified lottery game in which each ticket you purchase gives you one in a million chance of winning. Tickets are independent of each other (i.e. the outcome of one ticket does not effect the outcome of other tickets). 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? 100 1000 10000 100000 Suppose you buy 100 tickets every year for 10 years. What is the probability that you will have won the lottery at least once? Answer to 1 significant figure. Suppose there are 2,000,000 people like you i.e. 2,000,000 people who buy 100 tickets every year for 10 years. What is the chance that at least one of those 2,000,000 people wins the lottery two or more times?Explanation / Answer
a) a minimum number of ticket = 0.01/ 0.000001 = 10000`
b) Here, p = 0.000001
In a particular year probability of not winning is 10C0 * p^0 * (1 - p)^100 = 0.9999
Probability of not winning in any year is (0.9999)^10 = 0.999
Winning at least -0,999 = 0.001
c) Winning lottery in at least 1 year = 0.001
and not winning at all is 0.999
If there are 2 million people buying lottery
no one wins = 0.999^(2m) = 0
Hence, winning at least 1 is = 1 - 0 = 1