Question

You play roulette betting one dollar on the number 5 each time. The bet pays 35 to 1. You have a 1 in 38 chance to win. On average, you will lose playing this game and each play will cost you approximately _____ cents. (Round to the nearest cent)
Suppose you play roulette 64 times, betting a dollar on the number 5 each time, your expected net gain is______ dollars.
Using the short-cut, the SD for the box model is ______ dollars. Thus, the standard error of playing 64 times is ________ .
In 64 plays, you will lose ________ dollars, give or take  dollar ________.

Please show work. Thank you!!

Answer 1

a) The probability of winning here is given to be: 1/38

The winning price is 35 to 1.

Therefore the expected cost for each round in cents is computed here as:
= 100*(35*(1/38) - 1)

= 100*(-3/38) = 7.9 that is 8 cents to the nearest cent. Therefore 8 cents is the required answer here.

b) There will be an expected net loss as there is an expected loss in each play. This is computed here as:
= 64*(7.9)
= 505.6

Therefore 5.056 is the expected loss here.

c) Variance of each round is first computed as:
E(X2) = (-1)2 + 352*(1/38) = 33.2368
Var(X) = E(X2) - [E(X)]2 = 33.2368 - 0.0792 = 33.2306

Therefore, SD(X) =

Therefore for 64 rolls, this is computed as:
= 5.76*64 = 368.93

Therefore the required standard deviation for 64 rolls here is given as: 368.93

d) Therefore In 64 plays, we will lose 5.056 dollars give or take 368.93 dollars