Roulette, continued. You decide to play roulette 200 times, each time betting th

Question

Roulette, continued. You decide to play roulette 200 times, each time betting the Based on the information money if ou Win on fewer than the lose in Exercise 14.26, what is the probability that you will money? (Check that the Normal approximation is permissible and use it to find this probability. If your software allows, find the exact binomial probability and compare the two results.) In general, if you bet the same amount on red every time, you will lose money if you win on fewer than half of the plays. What do you think happens to the probability of making money the longer you continue to play?

Explanation / Answer

1) P(Red) = 18 out of 38 = 18/38

2) It is a binomial distribution with n=4, x varies from 0 to 4, p =18/38 , q=20/38

P(X = 0) = 4C0 (18/38)^0 *(20/38)^4

P(X = 1) = 4C1 (18/38)^1 *(20/38)^3

P(X = 2) = 4C2 (18/38)^2 *(20/38)^2

P(X = 3) = 4C3 (18/38)^3 *(20/38)^1

P(X = 4) = 4C4 (18/38)^4 *(20/38)^0

3) P(Break even) =

P(X = 2) = 4C2 (18/38)^2 *(20/38)^2 = 6*(18/38)^2 *(20/38)^2 =0.37

4 P(Lose) =P(X= 0)+ P(X=1) + P(X=2) = 4C1 (18/38)^1 *(20/38)^3 + 4C0 (18/38)^0 *(20/38)^4 +4C2 (18/38)^2 *(20/38)^2 = 0.725

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