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alexnunez07
10.06.2020 •
Mathematics
A state offers two lottery games, WinOne and PlayBall. Both games cost $2 per ticket.
In WinOne, the player picks a single letter from A to J and a single digit from 0 to 9. If both the letter and the digit match the letter and the digit picked on that day, the player wins $150.
In PlayBall, the player picks a single letter from A to T and a single digit from 0 to 9. If both the letter and the digit match the letter and the digit picked on that day, the player wins $280.
If the prize for WinOne were increased to $200 for matching both the letter and the digit, what would the expected value be?
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Ответ:
The price of the ticket = $1
Prize amount = $250
If a player wins, he will be winning $249 as the price is not paid back along with the prize amount. He is spending $1, getting back $250, so the net amount he is getting back is $249.
Now we have to find the probability of winning and losing.
Number of letters from A to T = 20
Number of digits from 0 to 9 = 10
Probability of picking up the same letter that was picked on that day = 1/20
Probability of picking up the same number that was picked on that day = 1/10
Thus, the Probability of picking up the same letter and same number that was picked on that day =
Thus, the probability of winning = 1/200
The probability of losing = 1 - 1/200 =99/200
The expected value E for the PlayBall lottery will be:
E = 1/200 (249) - 199/200
E = 1/4
E = 0.25
0.25
Ответ: