Question

Assuming you have to pay $6.00 to play the game, explain what happens in the long run. (Is it a good idea to play the game

Answer 1

Kindly check explanation

Step-by-step explanation:

We create a probability distribution for the play and winning :

Possible winning, X = 0, 7, 20

Probability of winning :

Sum of 2 die rolls ; sample space = 6² = 36

P(winning 0) = (sum ≠ 2,3,5 or 6)/ sample space = 24 / 36 = 2/3

P(winning 20) = (sum = (2 or 3) / Sample space) = 9 / 36 = 1/4

P(winning 7) = (sum = (5or6) / sample space) = 3 / 36 = 1/12

Distribution table :

X _____ 0 _______ 7 _____ 20

P(x) ___ 2/3 _____ 1/4 ____ 1/12

Expected value of the game ; E(X) ;

E(X) = Σx*p(x)

E(X) = (0*2/3) + (7*1/4) + (20*1/12)

E(X) = 0 + 1.75 + 1.6667

E(X) = 3.417

E(X) = 3.42

This means the mean winning after a long play is expected to be $3.42

To know if the game should be paku in the long run : we calculate the payoff

Expected Value - cost of paly

Cost of play = $6

Payoff = 3.42 - 6 = - 2.58

Since, payoff is negative, the game should not be played.