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Quantify the likelihood of multiple outcomes. Instantly calculate independent, dependent, and mutually exclusive events with exact precision. This free online tool allows you to calculate probabilities quickly and accurately. No sign-up or installation required.
Humans are notoriously terrible at intuitively grasping probability. We suffer from cognitive biases that make us fear statistically unlikely events (like shark attacks) while ignoring highly probable dangers. Probability theory is the branch of mathematics that strips away human emotion and replaces it with cold, hard fractions.
Probability is always expressed as a number between 0 and 1 (or 0% to 100%). A probability of 0 means the event is mathematically impossible. A probability of 1 means the event is absolutely certain to happen. The closer a number gets to 1, the more likely the event is to occur.
To accurately calculate the likelihood of multiple things happening, you must first determine how the events relate to one another. There are three primary classifications:
The outcome of the first event has absolutely zero effect on the second event. For example, flipping a coin twice. Getting "Heads" on the first flip does not change the 50/50 odds of getting "Heads" on the second flip.
The outcome of the first event permanently changes the odds of the second event. For example, drawing an Ace from a deck of cards, and keeping it. The odds of drawing a second Ace drop because there are now fewer Aces and fewer total cards.
Events that absolutely cannot happen at the exact same time. For example, rolling a single standard die. You can roll a 5, or you can roll a 6, but it is physically impossible to roll a 5 and a 6 simultaneously on one die.
One of the most destructive misconceptions in probability is the Gambler's Fallacy (also known as the Monte Carlo fallacy).
Imagine you are at a casino watching a roulette wheel. The ball has landed on "Black" five times in a row. A crowd gathers, convinced that the next spin must be "Red" because it is "due." This is mathematically false. A roulette wheel has no memory. The spins are entirely Independent Events. The odds of hitting Red on the sixth spin are exactly the same as the odds on the first spin. The universe does not auto-correct to balance out short-term streaks.
Answers to common questions regarding statistical likelihood, theoretical vs experimental probability, and "OR" vs "AND" mechanics.