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?

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 = 

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

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