Question

In a Vegas Casino game, if a player rolls two dice and gets a sum of 2 or 12, she wins $20. If a person gets a sum of 7, she wins $5. The cost to play the game is $3. Find the expectation of the game.

Answer 1

P[ Getting a sum of 2] = P[ Both die results in 1] =

Similarly P[ getting a sum of 12] = P[Both die results in 6] =

So, P[ Getting a sum of 2 or sum of 12] =  

Now, If we roll a die, there are 36 possible combinations .

Out of which 6 results in a sum of 7 , namely :

( 1,6 ), ( 2,5),( 3,4) ,(4,3),(5,2),(6,1)

So, P[ Getting a sum of 7 ] =

Let X be the value of the game .

Then X = 20 with probability 1/18

= 5 with probability 1/6

= 0 with probability 14/18 [ 1 - 1/18 -1/6 ]

So,

But she has to pay $ 3 for the game .

So, on an average her gain is $( 1.944-3) = -1.056

i.e The expected gain of the game is $ -1.056