Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

What is the difference between independent and mutually exclusive events?

Independent events are events where the outcome of one does not affect the outcome of the other (e.g., flipping a coin twice). Mutually exclusive events are events that cannot happen at the same time (e.g., rolling a 2 and a 3 on a single die roll).

How is the probability of 'A and B' calculated?

For two independent events, the probability of both A and B occurring is calculated by multiplying their individual probabilities: P(A and B) = P(A) × P(B).

Probability Calculator (Single & Multiple Events)

How Does This Calculator Work?

This calculator determines the likelihood of events based on fundamental probability formulas:

Probability of a Single Event: This is the most basic form. It's the ratio of desired outcomes to all possible outcomes.
Formula: P(A) = Favorable Outcomes / Total Outcomes
Probability of A and B (Independent Events): This calculates the chance of two separate events both happening. The outcome of one does not affect the other.
Formula: P(A and B) = P(A) × P(B)
Probability of A or B (Mutually Exclusive Events): This calculates the chance of either of two events happening, when they cannot both happen at the same time.
Formula: P(A or B) = P(A) + P(B)

The Surprising History of Probability

The formal study of probability theory has its roots not in a laboratory or university, but in the gambling halls of 17th-century France. A nobleman and avid gambler, the Chevalier de Méré, was puzzled by some apparent contradictions in games of dice. He posed his questions to the brilliant mathematician Blaise Pascal.

Pascal began a now-famous correspondence with another leading mathematician, Pierre de Fermat, to solve these problems. Through their letters, they laid down the fundamental principles of probability theory, establishing a mathematical framework for dealing with uncertainty. Their work on analyzing games of chance was the birth of a new branch of mathematics that is now essential to fields like insurance, finance, weather forecasting, and quantum mechanics.

Explore More Related Tools

While you're here, check out some of our other popular math and statistics calculators:

Statistics Calculator: Analyze data sets with mean, median, and mode.
Standard Deviation Calculator: Measure the spread of data.
Percentage Calculator: Probability is often expressed as a percentage.
Fraction Calculator: Probability is fundamentally a fraction.
Ratio Calculator: Compare odds and ratios.
Scientific Calculator: For advanced mathematical calculations.
Exponent & Root Calculator: Used in some probability distributions.
Logarithm Calculator: Useful in information theory and statistics.
GCF & LCM Calculator: Helpful for simplifying fractional probabilities.
Quadratic Equation Solver: Solve for unknowns in complex problems.

Frequently Asked Questions (FAQ)

How can I enter a probability like "1 in 6"?

You can enter probabilities as decimals (e.g., 0.1667) or as fractions (e.g., 1/6). The calculator will automatically convert the fraction to a decimal for the calculation.

What is the difference between probability and odds?

Probability is the ratio of favorable outcomes to *all possible* outcomes. Odds are the ratio of favorable outcomes to *unfavorable* outcomes. For example, the probability of rolling a 6 on a die is 1/6, but the odds of rolling a 6 are 1 to 5 (1:5).

What if two events are NOT mutually exclusive for an 'OR' calculation?

If two events can happen at the same time, the formula is more complex: P(A or B) = P(A) + P(B) - P(A and B). You must subtract the probability of both happening to avoid double-counting. This calculator handles the simpler, mutually exclusive case.

Probability Calculator

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