Show how you get the probabilities of winning all of the

Reference no: EM13608385

NYS Lottery's Pick 10 game: You pick 10 integers between 1 and 80 (including 1 and 80). The state picks 20 numbers. If all 10 of your numbers are among the state's 20 numbers you win $500,000. (Note that the state won't give $500,000 to each winner if too many people get 10 numbers among the 20 but we will assume that you always get the $500,000 if you match the numbers.) On the webpage you will find the following information:

Winning Numbers Matched	Prize	Chances of Winning
10	$500,000*	1 in: 8,911,711
9	$6,000	1 in: 163,381
8	$300	1 in: 7,384
7	$40	1 in: 621
6	$10	1 in: 87
0	$4	1 in: 22

a) Show how you get the probabilities of winning all of the above amounts.

b) Find the expected winnings.

c) Find the expected gain after paying $1 to play.

d) Why do you think that you win something if you match 0 numbers, rather than say winning something if you match 5 numbers?

Reference no: EM13608385

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