Question

Suppose someone gives you 4 to 1 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win ​$4 if you succeed and you lose ​$1 if you fail. What is the expected value of this game to​ you?

Should you expect to win or lose the expected value in the first​ game?

What can you expect if you play 200 ​times? Explain.​ (The table will be helpful in finding the required​ probabilities.)

Averaged over Averaged over 200 ​games, you should expect to win/lose $______ ?

Answer 1

Given that,

rolling two even numbers = { (2,2),(4,4),(6,6),(2,4),(4,2),(2,6),(6,2),(4,6),(6,4)}

P(rolling two even numbers ) =9/36 = 0.25

a.

expected value = (9/36)(4)+(-1)(27/36) =1-0.75=0.25 dollars

b.

Expected value of the game is positive and Expected value of the game is $0.250.

This means that in a long run you can expect to win an average of $0.250 for each game played.

This does not mean that player will win $0.250 on any single game.

Hence we can say that for the first game outcome of the game cannot be predicted.

c.

If I play 200 times I am expected to win 200 *0.25=$50