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.
There are ten possibilities for each number, so the probability of getting any one number is .1 or 1/10.
The probability of all events occurring (getting all three winning numbers) is found by multiplying the probability of the individual events.
Can you do that?
To find the expected winnings in the Numbers game, we need to calculate the probability of winning and losing, and then multiply it by the corresponding amount of winnings or losses.
In this case, there are a total of 1000 possible three-digit numbers from 000 to 999. Since all numbers are equally likely to come up, the probability of winning is 1 out of 1000, or 1/1000. Similarly, the probability of losing is 999 out of 1000, or 999/1000.
Now let's calculate the expected winnings:
Expected winnings = (Probability of winning * Amount won) + (Probability of losing * Amount lost)
Probability of winning = 1/1000
Amount won = $600.00
Probability of losing = 999/1000
Amount lost = $1.00
Expected winnings = (1/1000 * $600.00) + (999/1000 * (-$1.00))
Expected winnings = ($0.60) + (-$0.999)
Expected winnings = -$0.399
Therefore, your expected winnings in the Numbers game would be -$0.399, which means on average, you are expected to lose approximately $0.40 per game.