Find the expected value, ì, for the sum of two fair dice. The probability distribution for the sum of two dice is given in the table. ì = 1

2=1/36, 3=2/36, 4=3/36, 5=4/36, 6=5/36, 7=6/36, 8=5/36, 9=4/36, 10=3/36, 11=2/36, 12=1/36

the product of two fractions is 36/5 if one of them is 36/10 then find the fraction

To find the expected value, denoted as μ, for the sum of two fair dice, you need to multiply each possible sum by its corresponding probability and sum up the results. In this case, you have the probability distribution for the sum of two dice in the table.

The expected value formula is: μ = ∑ (X * P(X))

X represents the possible outcomes, and P(X) represents the probability of each outcome.

Let's calculate the expected value step by step:

For each value of X (from 2 to 12), multiply X by its corresponding probability:

For X = 2: 2 * (1/36) = 1/18
For X = 3: 3 * (2/36) = 1/6
For X = 4: 4 * (3/36) = 1/3
For X = 5: 5 * (4/36) = 5/18
For X = 6: 6 * (5/36) = 5/12
For X = 7: 7 * (6/36) = 7/12
For X = 8: 8 * (5/36) = 5/9
For X = 9: 9 * (4/36) = 2/3
For X = 10: 10 * (3/36) = 5/6
For X = 11: 11 * (2/36) = 11/18
For X = 12: 12 * (1/36) = 1/3

Now, sum up all the results:

1/18 + 1/6 + 1/3 + 5/18 + 5/12 + 7/12 + 5/9 + 2/3 + 5/6 + 11/18 + 1/3

Simplifying the fractions:

1/18 + 1/6 + 1/3 + 5/18 + 5/12 + 7/12 + 5/9 + 2/3 + 5/6 + 11/18 + 1/3 = 49/18

So, the expected value (μ) for the sum of two fair dice is 49/18, which is approximately 2.72.