On a roulette wheel, the probability of winning when

you pick a particular number is . Suppose you bet
$1.00 to play the game, and if your number is picked,
you get back $36.
a. Is this a fair game?
b. What would happen if you played this game a large
number of times?

a. The probability is not posted.

b. If you keep playing, it is most likely that you will lose your winnings back.

a. To determine if this game is fair, we need to compare the potential winnings with the probability of winning. In this case, the potential winnings are $36 if your number is picked, and the probability of winning is . The expected value (EV) of playing the game can be calculated using the following formula:

EV = (Potential Winnings) x (Probability of Winning) - (Amount Bet)

EV = ($36) x () - ($1.00)

Since we don't know the probability , it is impossible to determine if this is a fair game or not. To determine the fairness of the game, we would need to know the exact probability of winning.

b. If you play this game a large number of times, the concept of expected value becomes important. The expected value is the average amount you expect to win or lose per round. As you play more and more rounds, the average result should approach the expected value. In this case, if the game is fair, the expected value should be zero since you win with a probability of and lose otherwise.

However, without knowing the exact probability , we cannot determine the expected value or the long-term outcome of playing the game a large number of times. It's important to note that in gambling, the house always has an edge, meaning over a large number of plays, the expected value will likely be negative and you will lose money in the long run.