Problem

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

Solution

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: \[E = \frac{1}{6}+\frac{2}{6}+\frac{3}{6}+\frac{4}{6}+\frac{5}{6}+\frac{6}{6} = \frac{21}{6}\]

From Solvely APP
Source: https://solvelyapp.com/problems/BMi6Lpiv1q/

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