To find the expected value of a random event, you can follow these easy steps:

1. Identify Outcomes: First, list all the possible results of the event.

   For example, if you're rolling a die, the outcomes are 1, 2, 3, 4, 5, and 6.

2. Assign Probabilities: Next, figure out the chances of each outcome happening.

   If the die is fair, then each number has a chance of $\frac{1}{6}$.

3. Calculate Values: Now, multiply each outcome by its chance.

   For our die example, it looks like this:

   • $1 \times \frac{1}{6}$
   • $2 \times \frac{1}{6}$
   • $3 \times \frac{1}{6}$
   • $4 \times \frac{1}{6}$
   • $5 \times \frac{1}{6}$
   • $6 \times \frac{1}{6}$.

4. Sum Up: Finally, add all these results together to find the expected value.

   So, it would be: $\frac{1+2+3+4+5+6}{6} = 3.5$.

And that’s how you find the expected value!