If you bet $10 in a pick 4 lottery game, you either lose $10 or gain $7 comma 990. (the winning prize is $8 comma 000 , but your $10 bet is not returned, so the net gain is $7 comma 990 .) the game is played by selecting a four-digit number between 0000 and 9999. what is the probability of winning? if you bet $10 on 1234, what is the expected value of your gain or loss?

Question

Mathematics

Memphis Bernard

16 August, 09:43

If you bet $10 in a pick 4 lottery game, you either lose $10 or gain $7 comma 990. (the winning prize is $8 comma 000 , but your $10 bet is not returned, so the net gain is $7 comma 990 .) the game is played by selecting a four-digit number between 0000 and 9999. what is the probability of winning? if you bet $10 on 1234, what is the expected value of your gain or loss?

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Answers (1)

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Annalise Reid · Answer 1

The probability would be 1/10000. The expected value is a loss of $9.20.

There is exactly one number to match the winning 4 digit number in 10000 possible choices.

To find the expected value, we multiply each probability by its winnings or loss:

(1/10000) * (7990) = $0.799

(9999/10000) * (-10) = $-9.999

Adding these two, we get an expected loss of $9.20.