Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the formula for calculating expected value?

1. Sum of all outcomes

2. Multiply weights by their probabilities

3. Count the number of occurrences

4. Add all probabilities together

The correct answer is: Multiply weights by their probabilities

The formula for calculating expected value is indeed based on multiplying weights by their probabilities. In probability theory, the expected value (often denoted as E(X)) represents the average outcome of a random variable when the experiment is repeated many times. To find the expected value, you take each possible outcome of a random variable, multiply it by the probability of that outcome occurring, and then sum all these products together. This process weights each outcome by how likely it is to happen, which gives a more accurate representation of the average or "expected" result, especially in scenarios where outcomes have different probabilities. For example, if you have different outcomes of a game where some outcomes are more likely than others, simply summing all the outcomes or counting occurrences does not account for the relative likelihood of each outcome. By using probabilities to weigh the outcomes, you can effectively calculate what the average outcome would be over many trials. The other approaches do not yield the expected value. Summing outcomes does not consider their probabilities, while merely counting occurrences misses the idea of weighting by likelihood, and adding probabilities alone does not relate to the actual outcomes or the calculations necessary to find an expected value.