Expected value of including uncertainty

Okay, let's imagine that you have a big bag of candies and you don't know how many candies are in it. It could be 10 candies or it could be 100 candies. You don't know for sure.

Now, you really want to know how many candies you will have in the bag on average. That's where expected value comes in. Expected value helps us calculate what we think will happen on average.

To find the expected value of the number of candies in the bag, we need to do a little math. We start by calculating the probability of each possible outcome. The probability is like a guess of how likely something is to happen. For example, you might think there's a 50% chance there are 10 candies in the bag and a 50% chance there are 100 candies.

Now we multiply each probability by the number of candies in that outcome. So, we multiply 10 candies by 50% and 100 candies by 50%. This gives us 5 candies for the first outcome and 50 candies for the second outcome.

Finally, we add up all these values. 5 candies plus 50 candies equals 55 candies.

So, the expected value of the number of candies in the bag is 55. This means that if you repeat this experiment many times, you can expect to have around 55 candies on average.

Expected value helps us include uncertainty because it considers all possible outcomes and their probabilities. It helps us make a good guess of what will happen even when we don't know for sure. Remember, it's like making a prediction based on probabilities!