You play a gambling game with a friend in which you roll a die. If a 1 or 2 comes up, you win $8. Otherwise you lose $2. What is your expected value for this game?
2/6 * 8 - 4/6 * 2 = ?
To calculate the expected value for this game, we need to multiply each possible outcome by its corresponding probability and then sum them up.
In this case, there are two favorable outcomes (rolling a 1 or 2) with a probability of 2/6, since there are six possible outcomes (numbers 1, 2, 3, 4, 5, and 6) on a fair six-sided die. In each of these favorable outcomes, you win $8.
There are four unfavorable outcomes (rolling a 3, 4, 5, or 6) with a probability of 4/6. In each of these unfavorable outcomes, you lose $2.
Using these probabilities and outcomes, we can calculate the expected value as follows:
Expected Value = (Probability of winning × Amount won) + (Probability of losing × Amount lost)
Expected Value = (2/6 × $8) + (4/6 × -$2)
Expected Value = ($16/6) + (-$8/6)
Expected Value = $2.67 - $1.33
Expected Value = $1.34
Therefore, your expected value for playing this game is $1.34.
To calculate the expected value for this game, we need to multiply the value of each outcome by its corresponding probability and sum them up.
Here are the possible outcomes and their probabilities:
- Winning $8: The probability of rolling a 1 or 2 is 2/6, since there are two favorable outcomes out of six total possible outcomes (1, 2, 3, 4, 5, 6).
- Losing $2: The probability of rolling a number other than 1 or 2 is 4/6, since there are four unfavorable outcomes out of six total possible outcomes.
The calculations are as follows:
Expected Value = (Probability of Winning * Value of Winning) + (Probability of Losing * Value of Losing)
Expected Value = ((2/6) * $8) + ((4/6) * -$2)
Expected Value = ($16/6) + (-$8/6)
Expected Value = $8/6
Expected Value = $4/3
So, the expected value for this game is $4/3 or approximately $1.33.