Question

1. (3 pts) A roulette wheel has 38 pockets. One is num- bered 0, another 00, and the rest are numbered fro 1- to 36. Except for 0 and 00, which are colored green, the numbers on the roulette alternate between red and black. A bet is on red or black. Suppose you bet one dollar on red. If a red number comes up, you get your dollar back and win another dollar. If a black or green number comes up, you lose your dollar. In the box model, there are tickets showing ____ and ___ tickets showing 2. (3 pts) If you bet a dollar on a single number on the roulette and that number comes up, you get your dollar back and win 35 dollars. If any other number comes up, you lose your dollar. Gamblers say that a single number pays 35 to 1. In the box model, there are tickets showing - and- tickets showing Suppose you play roulette 50 times, betting a dollar on the number 17 each time, your net gain is like the sum of draws made at random with replacement from the box model above. 3. (4 pts) 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 dollars. humhar

Answer 1

1. In the box model 18 tickets showing 1 and 20 tickets showing -1.

2. In the box model 1 ticket showing 35 and 37 tickets showing -1.

The net gain is like the sum of 50 draws made at random with replacement from the box model above.

3. Here given that the winning chances are 1 in 5 i.e. probability of winning is 0.2. Given that you win 2 dollars if you win thus expected winnings are:

0.2*2 + 0.8*(-1) = -0.4.

Hence each play costs you 40 cents. I f you play 200 times then you can expect to lose 200*0.4 = 80 dollars.