Question

In the game of roulette, there is a wheel with 37 slots numbered with the integers from 0 to 36, inclusive. A player bets $3 and chooses a number. The wheel is spun and a ball rolls on the wheel. If the ball lands in the slot showing the chosen number, the player receives $3 plus 100$. Otherwise, the player loses the $3 bet. Assume that all numbers are equally likely. Determine the variance of the gain or loss per play.

Answer 1

Answer:-

Given that:-

In the game of roulette, there is a wheel with 37 slots numbered with the integers from 0 to 36, inclusive. A player bets $3 and chooses a number. The wheel is spun and a ball rolls on the wheel. If the ball lands in the slot showing the chosen number, the player receives $3 plus 100$. Otherwise, the player loses the $3 bet. Assume that all numbers are equally likely. Determine the variance of the gain or loss per play.

If f is the probability function for X, then

= P (player wins the best)

=P(ball lands on the number chosen by the player)

= P(player loses the best)

=P (ball does not land on the number chosen by the player)

The expected value of X is given by

Thus the expected loss per play is a approximately $ 6.22