The expected value is the balance point of probability as weight
What happens if you place the values a random variable X can take on a scale, weighted according to how likely each is to occur? The point where the scale balances exactly is the expected value E(X). Use the sliders to change the values and probabilities and watch the balance point move, then discover the real usefulness of expected value with a dice prize game.
A random variable X can take the value A or B. Use the slider to change the probability that A occurs. The size of each circle is the size of its probability, and the triangle (ā²) marks the position of the expected value E(X) = AĆP(A) + BĆP(B).
Value A8
Value B-4
Probability of A, P(A)30%
Roll a die: if it lands on 6, you win the prize; otherwise, you get nothing. What entry fee makes this game exactly "fair" ā no loss and no gain?