Question

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?

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.