Question

You roll a die. If it comes up a 2 or 3​, you win ​$300 If​ not, you get to roll again. If you get

a 2 or 3 the second​ time, you win $150 If​ not, you lose.

​a) Create a probability model for the amount you win.

​b) Find the expected amount​ you'll win.

​c) What should you be willing to pay to play this​ game?

Answer 1

P[ 2 or 3 ] = 2/6 = 1/3

P[ not getting 2 or 3 in first trial ] = 1 - P[ 2 or 3 ]

P[ not getting 2 or 3 in first trial ] = 1 - 1/3

P[ not getting 2 or 3 in first trial ] = 2/3

P[ getting 2 or 3 in second trial ] = P[ not getting 2 or 3 in first trial ]*P[ 2 or 3 ]

P[ getting 2 or 3 in second trial ] = (2/3)*(1/3)

P[ getting 2 or 3 in second trial ] = 2/9

​a) Create a probability model for the amount you win.

Amount	$300	$150	0	Total
Probability	1/3	2/9	1-1/3-2/9 = 4/9	1

b) Find the expected amount​ you'll win.

E(X) = (1/3)*300 + (2/9)*150 + 0*(4/9)

E(X) = 100 + 100/3 + 0

E(X) = 400/3

E(X) = 133.33

​c) What should you be willing to pay to play this​ game?

the maximum amount can be paid to play the game is $133.33