I am having trouble understand what is the expected value of rolling a die? I know that I would start by finding the probability of 1,2,3,4,5,6. But I do not know what to do after that?
Thanks!
The expected probability of rolling a die and landing on any number (1,2,3,4,5,6) would always be 1/6, because there are 6 possible outcomes, but only 1 will happen.
I'm not sure i understand the question...
To find the expected value of rolling a die, you would indeed start by finding the probability of each outcome (1, 2, 3, 4, 5, and 6) when rolling a fair die. Since a fair die has 6 equally likely outcomes, the probability of each outcome is 1/6.
After finding the probabilities, multiply each outcome by its corresponding probability. Then, sum up these products to find the expected value.
Let's calculate the expected value step by step:
1. Find the probability of each outcome:
- P(1) = 1/6
- P(2) = 1/6
- P(3) = 1/6
- P(4) = 1/6
- P(5) = 1/6
- P(6) = 1/6
2. Multiply each outcome by its corresponding probability:
- (1 * P(1)) + (2 * P(2)) + (3 * P(3)) + (4 * P(4)) + (5 * P(5)) + (6 * P(6))
Simplified:
- (1/6) + (2/6) + (3/6) + (4/6) + (5/6) + (6/6)
3. Sum up the products:
- 1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6
Simplifying the fractions and adding them up:
- 21/6
4. Simplify the fraction if necessary:
- 21/6 = 7/2
So, the expected value of rolling a fair die is 7/2 or 3.5.
Therefore, on average, you can expect the outcome of rolling a fair die to be around 3.5.