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Four possibly winning numbers for a lottery—AB-4536,
Chapter 3, Problem 180SE(choose chapter or problem)
Problem 180SE
Four possibly winning numbers for a lottery—AB-4536, NH-7812, SQ-7855, and ZY-3221— arrive in the mail. You will win 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?
Questions & Answers
QUESTION:
Problem 180SE
Four possibly winning numbers for a lottery—AB-4536, NH-7812, SQ-7855, and ZY-3221— arrive in the mail. You will win 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?
ANSWER:
Answer:
Step 1 of 1:
Four winning numbers for a lottery is which arrived in the mail. You will win a prize if the number matches one of the winning numbers on a list held by those conducting the lottery.
One first prize worth of , two second prizes worth of
each, and ten third prizes of $1000 each will be awarded.
To be eligible to win, you need to mail the lottery back to the company at a cost of 33 cents for postage.
Assuming that the numbers received were generated at random.
What is the expected winnings from the lottery, is it worth 33 cents to enter this lottery?
Let be the random variable which represents the winning of the lottery.
Hence we need to find the