Mathematics
Expected Value in Probability
Quick fact
Expected value is like a 'weighted average'—it takes into account both the possible outcomes and their likelihoods to give a single numerical estimate of what might happen on average.
Why this is interesting
Imagine you're playing a game where you can win or lose money based on the roll of a die. How could you predict whether it's worth playing in the long run? The answer lies in expected value.
Read the full explanation
Understanding Expected Value in Probability
In probability, the expected value helps us figure out what we can expect as an average result from a random event. For example, if you bet $1 on a coin flip with a 50% chance of winning $2, your expected value is (0.5 × $2) + (0.5 × -$1) = $0.50 per flip. This means, over many flips, you'd expect to gain about 50 cents per game.
A deeper explanation
Expected value in probability is calculated by multiplying each possible outcome of a random event by the probability that outcome will occur, and then summing all those values. It provides a way to predict what an average result might look like over many repeated trials. This concept is essential because it allows us to make decisions based on long-term averages rather than short-term luck.