Probability Calculator
Probability - Solve mathematical problems with step-by-step solutions.
Probability Calculator
For Independent Events
Probability Basics
This calculator assumes events are independent.
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) - P(A and B)
How the Probability Calculator Works
Probability is the measure of how likely an event is to occur. It's expressed as a number between 0 and 1, where 0 means impossible and 1 means certain. Probabilities can also be expressed as percentages (0% to 100%) or fractions.
Basic Formula
P(A) = Favorable outcomes / Total outcomes
Probability always falls between 0 and 1 (or 0% and 100%). P = 0 means impossible, P = 0.5 means equally likely, and P = 1 means certain.
Types of Probability
Simple Probability
The probability of a single event occurring.
Example: Rolling a 4 on a six-sided die: P = 1/6 ≈ 0.167 or 16.7%
Compound Probability
The probability of two or more events occurring.
- AND (Independent): P(A and B) = P(A) × P(B)
- OR (Mutually Exclusive): P(A or B) = P(A) + P(B)
Conditional Probability
The probability of an event occurring given that another event has occurred.
P(A|B) = P(A and B) / P(B)
Common Examples
Coin Flip
P(Heads) = 1/2 = 0.5 = 50%
Two equally likely outcomes
Drawing a Card
P(Ace) = 4/52 ≈ 0.077 = 7.7%
4 aces in a 52-card deck
Two Dice Sum
P(Sum = 7) = 6/36 ≈ 0.167 = 16.7%
Six ways to get 7 out of 36 outcomes
Weather Forecast
P(Rain) = 0.3 = 30%
Based on historical data and models
Frequently Asked Questions
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