A fair die is rolled. What is the expected value of the number that shows up?

Question

Accepted Answer

Step:1 ：We first need to know the probability distribution of the outcomes. For a fair die, the outcomes are equally likely. So for each outcome from 1 to 6, the probability is (frac{1}{6}).Step:2 ：The expected value is calculated by multiplying each outcome by its probability and then summing these products. So the expected value E is given by the formula: [E = (1)left(frac{1}{6}right)+(2)left(frac{1}{6}right)+(3)left(frac{1}{6}right)+(4)left(frac{1}{6}right)+(5)left(frac{1}{6}right)+(6)left(frac{1}{6}right)]Step:3 ：We carry out the multiplication and addition: [E = frac{1}{6}+frac{2}{6}+frac{3}{6}+frac{4}{6}+frac{5}{6}+frac{6}{6} = frac{21}{6}]

Answer

Step: 1 ：We first need to know the probability distribution of the outcomes. For a fair die, the outcomes are equally likely. So for each outcome from 1 to 6, the probability is (frac{1}{6}).Step: 2 ：The expected value is calculated by multiplying each outcome by its probability and then summing these products. So the expected value E is given by the formula: [E = (1)left(frac{1}{6}right)+(2)left(frac{1}{6}right)+(3)left(frac{1}{6}right)+(4)left(frac{1}{6}right)+(5)left(frac{1}{6}right)+(6)left(frac{1}{6}right)]Step: 3 ：We carry out the multiplication and addition: [E = frac{1}{6}+frac{2}{6}+frac{3}{6}+frac{4}{6}+frac{5}{6}+frac{6}{6} = frac{21}{6}]

A fair die is rolled. What is the expected value of the number that shows up?

Answer

Popular Problems