Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $3.00 for rolling a 6 or a 3, nothing otherwise. What is your expected value?
1/6X1/6= 1/36=.0277
To calculate the expected value, you need to determine the probability of each outcome and multiply it by the corresponding value. In this case, the outcome values are $0.00 for anything other than 3 or 6, and $3.00 for rolling a 3 or 6.
Let's break it down step by step:
1. Calculate the probabilities:
- There's a 1 in 6 chance of rolling a 3 (since a fair die has 6 sides and only one side has a 3).
- Similarly, there's a 1 in 6 chance of rolling a 6.
2. Calculate the expected value:
- Multiply the probability of each outcome by its corresponding value, and sum them together.
- For rolling a 3 or 6: (1/6) * $3.00 = $0.50.
- For any other result: (4/6) * $0.00 = $0.00.
- Add these values together: $0.50 + $0.00 = $0.50.
Therefore, the expected value of this game is $0.50, meaning you can expect to earn $0.50 each time you play.
To calculate your expected value, you need to multiply the value of each outcome by its probability and then sum them all up.
In this case, the possible outcomes are rolling a 6 or a 3, which each pay $3.00, and rolling any other number, which pays $0.00.
The probability of rolling a 6 or a 3 on a fair die is 2 out of 6, or 2/6 = 1/3. Thus, the probability of rolling any other number is 1 - 1/3 = 2/3.
Now, let's calculate the expected value step-by-step:
1. Value of rolling a 6 or a 3: $3.00 x (1/3) = $1.00
2. Value of rolling any other number: $0.00 x (2/3) = $0.00
To find the expected value, sum up the two outcomes:
Expected value = $1.00 + $0.00 = $1.00
Therefore, your expected value is $1.00.