Answer:
To find the expected payback, you need to consider the probability of winning and losing, along with the corresponding payouts.
Probability of Winning (Pwin): There is 1 winning number, and there are 1000 possible numbers (0 to 999). Therefore, the probability of winning 1/1000
Probability of Losing (Plose): Since you bet on a specific number, there are 999 losing numbers. The probability of losing is
999/1000
Payout for Winning (Payoutwin): If you win, you get $500.
Payout for Losing (Payoutlose): If you lose, you lose your $5 bet.
Now, you can calculate the expected payback using the formula:
Expected Payback= (1/1000x$500)+(999/1000x(-$5))
Expected Payback=Pwin × Payoutwin + Plose × Payoutlose
Expected Payback = $0.50-$4.995
Expected Payback= -$4.495
The expected payback for this game is approximately -$4.495. This means, on average, you can expect to lose $4.495 for each $5 bet over the long run. Keep in mind that this is an average, and individual outcomes may vary.
Explanation: