Question

a modified game of roulette cost 3 dollars to play. if the roulette wheel lands on a "0" the player gets nothing back, if the spinner lands on"+2" the player gets two dollars back and if the spinner lands on "+5" the player gets five dollars back. What is the expected value of this game? What is the fair cost of this game?

Answer 1

Solution

Back-up Theory

If a discrete random variable, X, has probability function, p(x), then

Expected value = Σ{x.p(x)} summed over all possible values of x…................................................…. (1)

Now to work out the solution,

Let X = the amount the player gets back. Then,

X = 0 if roulette wheel lands on ‘0’

   = 2 if roulette wheel lands on ‘+ 2’

    = 5 if roulette wheel lands on ‘+ 5’

Assuming that roulette wheel lands on ‘0’, ‘+ 2’ and ‘+ 5’ with equal probability,

Vide (1),

expected value of this game = {0 x (1/3)} + {2 x (1/3)} +{5 x (1/3)} = 7/3 = $2.33 Answer 1

Fair game would mean that the player on an average neither wins nor loses. So, the   

fair cost of this game = $2.33 Answer 2

DONE