Question

Suppose someone gives you

1414

to

44

odds that you cannot roll two even numbers with the roll of two fair dice. This means you win

​$1414

if you succeed and you lose

​$44

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

200200

​times? Explain.​ (The table will be helpful in finding the required​ probabilities.)

LOADING...

Click the icon to view the table.

What is the expected value of this game to​ you?

​$

 

nothing

Should you expect to win​ (or lose) an amount equal to the expected value in the first​ game?

​Yes, you can expect to win​ (or lose) the expected value in the first game.

​No, the outcome of one game cannot be predicted.

What can you expect if you play

200200

​times?

​$

 

nothing

Explain this result.

Averaged over

Answer 1

Answer : Suppose someone gives you 14 to 4 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win​$14 if you succeed and you lose ​$4 if you fail.

Solution :

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

so the number of favourable outcomes is 9, when we are rolling a two fair dice total number of outcomes is 36

P(rolling two even numbers) = number of favourable outcomes / number of total outcomes

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

Therefore, probability of winning = 0.25

Probability of losing = 1 - 0.25 = 0.75

** Expectedvalue of the game = (Probability of winning * value you will get when you win) + (Probability of losing * value you will pay if you loose)

As given you will get $14 if you win and you will pay $4 if you loose

Expected value of the game = (0.25*$14) + (0.75*(-$4))

Expected value of the game = $ 3.5 - $ 3 = $ 0.50  

** Expectedvalue of the game is positive. that is $0.50. This means you can expect to win an average of $0.50 for each game played. This does not mean that player will win $0.50 on any single game.

Hence, No outcome of the one game cannot be predicted.

** The expected value if game is played for 200 times :

the expected value is = 200 * $ 0.50 = $ 100

Hence if 200 games are played you should expect to win $100

Averaged over 200 games, you should expect to win $100.