How to Calculate Probability
Probability is the mathematical measurement of how likely an event is to happen. It is calculated by taking the number of favorable outcomes (what you want to happen) and dividing it by the total number of possible outcomes.
You want to roll a 5 or a 6 on a standard six-sided die.
• Favorable Outcomes: 2 (rolling a 5, or rolling a 6)
• Total Possible Outcomes: 6 (rolling a 1, 2, 3, 4, 5, or 6)
• Math: 2 / 6 = 33.33% chance.
Probability vs. Odds
People often use the words "probability" and "odds" interchangeably, but in mathematics and betting, they mean two completely different things.
Probability
Compares the favorable outcomes against the TOTAL possible outcomes. It is usually expressed as a percentage or a fraction.
Example: The probability of pulling a Heart from a deck of cards is 13/52 (or 25%).
Odds
Compares the favorable outcomes directly against the UNFAVORABLE outcomes. It is usually expressed with a colon (X:Y).
Example: The odds of pulling a Heart are 13:39 (which simplifies to 1:3). For every 1 heart, there are 3 non-hearts.
Multiple Independent Events
When dealing with multiple events that do not affect each other (called Independent Events), the math changes depending on what you are looking for:
- AND (Multiplication Rule): If you want Event A and Event B to happen, you multiply their probabilities together. (e.g., Flipping heads AND rolling a 6).
- OR (Addition Rule): If you want Event A or Event B to happen, you add their probabilities together, then subtract the probability of them both happening at the same time so you don't double-count.