Four possible winning numbers for a lottery- AB-4536, NH-7812, SQ-7855, and ZY-3
ID: 2965108 • Letter: F
Question
Four possible winning numbers for a lottery- AB-4536, NH-7812, SQ-7855, and ZY-3221- arrive in the mail. You wil a prize if one of your numbers matches one of the winning numbers contained on a list held by those conducting the lottery. One first prize of $100,000, two second prizes of $50,000 each, and ten third prizes of $1000 each will be awarded. To be eligible to win, you need to mail the coupon back to the company at a cost of .33 for postage. No purchase is required. From the structure of the numbers that you received, it is obvious the numbers sent out consist of two letters followed by four digits. Assuming that the numbers you received were generated at random, what are your expected winnings from the lottery? Is it worth .33 to enter this lottery?
Explanation / Answer
Total number of possible lottery tickets = 26*26*10*10*10*10 (for each alphabet and digit in the ticket number)
= 6,760,000 combinations
Total possibility of winning $100,000 = 1 out of 6,760,000
Total possibility of winning $50,000 = 2 out of 6,760,000
Total possibility of winning $ 10,000 = 10 out of 6,760,000
Total expected earnings = 100000/6760000 + 2*50000/6760000 + 10*10000/6760000
= .03 (or 3.1 cents)
33 cents > 3.1 cents
Therefore the odds are against you.
It is not worth to spend .33 to enter the lottery
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