Question

A gambling game called "Rollo" pays 3 to 1, and you have a 1 in 6 chance of winning on any given play. Find the probability that you lose a total of $20 or more if you bet one dollar on each of 200 plays of Rollo. Give your answer in percent, without the percent sign.
Describe the details of your calculation in the previous problem. Describe the box model (how many tickets in the box model, what numbers are on the tickets, how many of each?). You do not have to write complete sentences. Give the average and SD for the box. Give the expected total winnings and the SE for the total winnings. Give the appropriate z value.

Answer 1

Given data:

S = X1 + X2+......+Xn

Where X is his earning

P(X = 3) = 1/6

P(X = -1) = 5/6

E(X) = 3*1/6 - 1*5/6
= -1/3

E(X^2) = 2.333
sd = 1.4907

E(S) = n E(X) = 200 * (-1/3) = -66.67
sd(S) = sqrt(n) * sd(X) = sqrt(200) * 1.4907 = 21.0817

S follows normal distribution as n > 30
P(S < -20)
= P(Z < (-20 + 66.67)/21.0817)
= P(Z < 2.2137)
= 0.9866