In a game, you have a 1/27 probability of winning $100 and a 26/27 probability of losing $4. What is your expected value?

To find the expected value, we multiply each outcome by its probability and then sum them up.

In this case, we have two outcomes:
- Winning $100 with a probability of 1/27
- Losing $4 with a probability of 26/27

Expected Value = (Probability of winning * Value of winning) + (Probability of losing * Value of losing)

Expected Value = (1/27 * $100) + (26/27 * -$4)

To calculate this, we can simplify the fractions:

Expected Value = $100/27 + (-$104/27)

To combine the fractions, we have to find a common denominator, which is 27:

Expected Value = ($100 - $104)/27

Simplifying, we get:

Expected Value = -$4/27

Therefore, the expected value in this game is -$4/27.

Expected value is the sum of the product of all possible outcomes and the respective probability.

Example of rolling one six-sided die:
Payout equals the number appearing on top face.
expected value =
1*1/6+2*1/6+3*1/6+4*1/6+581/6+6*1/6
=3.5