Question

Suppose that in a day, a casino receives 2500 bets on a certain color(red or black) on one particular roulette wheel. Each bet is only a dollar bet. The house(casino) has 20 in 38 chances to win. Estimate the chance that the house will win at least 100 dollars. Write your answer as a decimal.Using z score . Note: In practice, a casino has many roulette wheels and many bets are much more than a dollar. The house always win!

Answer 1

Let $X_i$ be the random variable denoting the amount the house wins on the i^th bet.

So, X_i = 1 with probability 20/38 and X_i = -1 with probability 18/38.

E(X;) - 2018 1 1:) = 38 38 = 10

E(X) = 1

Var(X)= E(x}) – E(X;)2 = 1 - 1 = 500

Let   $T = \sum_i X_i$

Now, using central limit theorem,

11 T-NG 360 x 2500, 2 x 2500

T N (131.579,2493.075)

(T – 131.579 P(T > 100) = PO 2493.075 100 – 131.579 2 493.075

(T - 131.579 P(T > 100) = PO 2493.075 > -0.6324) = (0.6324) = 0.7357