Question

Suppose you make a dollar bet on a game in which there is a 1 in 5 chance to win. If you win, you win two dollars. On average, you will lose playing this game and each play costs you _______ cents. If you play 200 times, you can expect to lose around _______  dollar 

.

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.

 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 _______ dollars. 

Answer 1

1)

• proability of winning i.e p = 1/5 = 0.2

  proability of losing = 1- 0.2 = 0.8

  amount lost if you lose the bet is 1 and amount won if you won the bet is 2

  expected profit = (-1)*0.8 +0.2*2 = -0.8+0.4 = -0.4

  so expected loss = 0.4

  so each play costs you $0.4 i.e 40 cents

  expected loss if you play 200 times = 200*expected loss for each play = 200*0.4 = 80 dollars