Question

Suppose someone gives you 15 to 4 odds that you can't roll 2 even numbers with the roll of 2 fair dice. This means you win $15 if you succeed and you lose $4 if you fail. What is the expected value of this game to you? What can you expect if you play 200 times?

Answer 1

You can expect to make more money. There are 3 possibilities for this answer this question which gives each one 33.33% chance. Only one of these possibilities will leave you with money.

I hope that this helps

Answer 2

Expected Value: $0.75

Expected win after 200 plays: $150

Explanation:

Succeed: roll two even values

Possibilities to succeed:

2, 2

2, 4

2, 6

4, 2

4, 4

4, 6

6, 2

6, 4

6, 6

They make 9 possible ways. There are 36 possible outcomes after rolling 2 dice . Therefore:

Probability of winning = 9/36 = 0.25

Probability of losing = 1 - 0.25 = 0.75

The expected value is computed as follows:

probability of winning * the value you get when you win + probability of losing* value you get when you lose

Expected Value = 0.25 * $15 + 0.75*(-$4) = $0.75

Notice that the $4 is negative because it is a loss .

If you play 200 times your expected win is: 200* $0.75 = $ 150