Numbers is a game where you bet $1 on any three-digit number from 000 to 999. If your number
comes up, you get $600.00, otherwise you lose the $1. Find your expected winnings if all numbers
are equally likely to come up.
To find your expected winnings, you need to multiply the probability of winning by the amount you can win and subtract the probability of losing multiplied by the amount you lose.
In this case, the probability of winning is 1 out of 1000 because there are 1000 possible three-digit numbers (000 to 999), and you are betting on one of them.
So, the probability of winning is 1/1000.
The amount you can win is $600.00.
The probability of losing is 999 out of 1000 since there are 999 numbers that you can lose on.
The amount you lose is $1.00.
Now we can calculate the expected winnings:
Expected winnings = (Probability of winning * Amount you win) - (Probability of losing * Amount you lose)
Expected winnings = (1/1000 * $600.00) - (999/1000 * $1.00)
Expected winnings = $0.60 - $0.999
Expected winnings = -$0.399
Therefore, your expected winnings are -$0.399 or a loss of $0.40. This means that on average, you would expect to lose 40 cents per game if all numbers are equally likely to come up.
there are 1000 numbers from 000 to 999
so the prob of any one coming up is 1/1000
the expected winning = 1/1000(600) = .60 or 60¢.
(not smart to play that game)