Problem 100E

The business of casino gaming. Casino gaming yields over $35 billion in revenue each year in the United States. In Chance (Spring 2005), University of Denver statistician R. C. Hannum discussed the business of casino gaming and its reliance on the laws of probability. Casino games of pure chance (e.g., craps, roulette, baccarat, and keno) always yield a “house advantage.” For example, in the game of double-zero roulette, the expected casino win percentage is 5.26% on bets made on whether the outcome will be either black or red. (This implies that for every $5 bet on black or red, the casino will earn a net of about 25..) It can be shown that in 100 roulette plays on black/red, the average casino win percentage is normally distributed with mean 5.26% and standard deviation 10%. Let x represent the average casino win percentage after 100 bets on black/ red in double-zero roulette.

a. Find P(x > 0). (This is the probability that the casino wins money.)

b. Find P(5 < x < 15).

c. Find P(x < 1).

d. If you observed an average casino win percentage of -25, after 100 roulette bets on black/red, what would you conclude?

Solution:

Step 1 of 5:

Let, x = the average casino win percentage after 100 bets on black/red in double- zero roulette

Let x follows the Normal distribution with the probability density function is

f(x) =

Where, = 5.26 and

= 10.