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PLEASE!!!!!!!!!! HELP NEEDED QUICK
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 cost of a PlayBall lottery ticket were changed to $1 and the prize to $250, what would the expected value be?
A)$-0.85
B)$-0.25
C)$0.25
D)$0.75

Respuesta :

We have to find the expected value for the PlayBall lottery. 
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 = [tex] \frac{1}{20}* \frac{1}{10}= \frac{1}{200} [/tex]

Thus, the probability of winning = 1/200

The probability of losing = [tex]1- \frac{1}{200}=\frac{199}{200} [/tex]

The expected value E for the PlayBall lottery will be:

[tex]E= \frac{1}{200}(249)- \frac{199}{200}(1) \\ \\ E= \frac{1}{4} \\ \\ E=0.25 [/tex]

Thus, the option C gives the correct answer

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