If a person rolls two dice and obtain a sum of 2 or 12, he wins $15. Find the expectation of the game if the person pays $5 to play.

yuhki
Nov 21, 2014

#1**+5 **

I don't know how to do this

BUT

Well the probablility of getting double 2 or double 6 is 2/36 = 1/18

So he has 1/18 chance of winning $15

and a 17/18 chance of losing $5

So maybe

$$\left({\frac{{\mathtt{1}}}{{\mathtt{18}}}}{\mathtt{\,\times\,}}{\mathtt{15}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{17}}}{{\mathtt{18}}}}{\mathtt{\,\times\,}}{\mathtt{5}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{35}}}{{\mathtt{9}}}} = -{\mathtt{3.888\: \!888\: \!888\: \!888\: \!888\: \!9}}$$

So the person should expect to lose $3.89

This probably is not correct. I am totally guessing. Sorry.

If you find out how it is done please let us know. If I find out I will post it on this thread.

Someone else probably knows how to do it. I shall ask around. :))

Melody
Nov 22, 2014

#2**+5 **

This is correct, Melody.......!!!!

Another way to look at this is.......call the amount of money the person bets = B...........and call the amount of money he wins = 3B

So the expected value of * any* bet is

3B(1/18) - B(17/18) =

3B/18 - (17B)/18 =

-(14B)/18 =

-.7778 B

In other words......the player stands to lose about 78 cents on each dollar he bets........

(Contrast this to the game of roulette where, on the "American Wheel," the player stands to lose a little more than 5 cents per dollar bet on any spin !!! )

CPhill
Nov 22, 2014