Probability Of Multiple Events Calculator

Probability Formula:

\[ P(all) = \prod P(event_i) \]

Combined Probability:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Probability of Multiple Events?

The probability of multiple independent events occurring together is the product of their individual probabilities. This fundamental concept in probability theory applies when the occurrence of one event doesn't affect the others.

2. How Does the Calculator Work?

The calculator uses the probability multiplication rule:

\[ P(all) = P(event_1) \times P(event_2) \times \cdots \times P(event_n) \]

Where:

\( P(all) \) — Probability of all events occurring together
\( P(event_i) \) — Probability of each individual event (must be between 0 and 1)

Explanation: For independent events, the combined probability is simply the product of each event's probability.

3. Importance of Combined Probability

Details: Calculating combined probabilities is essential in statistics, risk assessment, decision making, and many scientific fields where multiple independent factors contribute to an outcome.

4. Using the Calculator

Tips: Enter probabilities as decimal values between 0 and 1, separated by commas. For example: "0.5, 0.3, 0.8".

5. Frequently Asked Questions (FAQ)

Q1: What if my events are not independent?
A: This calculator assumes independence. For dependent events, you would need to use conditional probabilities.

Q2: Can I use percentages instead of decimals?
A: No, you must convert percentages to decimals (e.g., 50% = 0.5) before entering them.

Q3: What's the difference between AND and OR probabilities?
A: This calculator computes AND probability (all events occurring). OR probability (at least one occurring) uses a different formula.

Q4: How many probabilities can I enter?
A: You can enter as many as needed, but all must be valid probabilities between 0 and 1.

Q5: What does a result of 0 mean?
A: It means the combination of events is impossible (at least one event had probability 0).