Probability Calculator
Calculate probability, odds, and likelihood of events
Single Event Probability
Example: Rolling a 6 on a die = 1 favorable outcome out of 6 total outcomes
Results
Multiple Events (A and B)
Note: These calculations assume independent events. For dependent events, use conditional probability.
🎲 Quick Answer
With 1 favorable outcome(s) out of 6 total, the probability is 0.1667 or 16.67%. The odds are 1:5 (for:against).
Dr. Snezana Lawrence
Mathematical Historian
15+ years experience
PhD from Yale University. Published mathematical historian ensuring precision in all calculations.
Education
PhD in Mathematical History - Yale University
📑 Table of Contents
🤔 What is Probability?
Probability is a measure of the likelihood that an event will occur. It's expressed as a number between 0 and 1, where:
Impossible Event
Will never happen
Equally Likely
50% chance
Certain Event
Will always happen
Probability vs. Odds
Probability: Favorable outcomes ÷ Total outcomes (e.g., 1/6)
Odds: Favorable outcomes : Unfavorable outcomes (e.g., 1:5)
📐 Probability Formula
Basic Probability Formula
P(A) = Number of favorable outcomes / Total number of outcomes
Key Formulas
Complement Rule
P(not A) = 1 - P(A)
Addition Rule (OR)
P(A or B) = P(A) + P(B) - P(A and B)
Multiplication Rule (AND) - Independent Events
P(A and B) = P(A) × P(B)
Conditional Probability
P(A|B) = P(A and B) / P(B)
📊 Types of Probability
Theoretical Probability
Based on reasoning and analysis. Assumes all outcomes are equally likely.
Example: Probability of rolling a 6 = 1/6
Experimental Probability
Based on actual experiments and observations.
Example: Rolled a die 100 times, got 6 eighteen times = 18/100
Independent Events
One event doesn't affect the other.
Example: Flipping a coin twice
Dependent Events
One event affects the probability of another.
Example: Drawing cards without replacement
📏 Probability Rules
Range Rule
Probability is always between 0 and 1: 0 ≤ P(A) ≤ 1
Sum Rule
Probabilities of all possible outcomes sum to 1
Complement Rule
P(A) + P(not A) = 1
Mutually Exclusive Events
If events can't happen together: P(A or B) = P(A) + P(B)
🎯 Common Probability Examples
🎲 Rolling a Die
P(any number) = 1/6 ≈ 16.67%
P(even) = 3/6 = 1/2 = 50%
P(less than 5) = 4/6 ≈ 66.67%
🪙 Flipping a Coin
P(heads) = 1/2 = 50%
P(2 heads in row) = 1/4 = 25%
P(3 heads in row) = 1/8 = 12.5%
🃏 Drawing Cards
P(ace) = 4/52 ≈ 7.69%
P(heart) = 13/52 = 25%
P(face card) = 12/52 ≈ 23.08%
🎰 Lottery
Pick 6 from 49:
P(jackpot) = 1/13,983,816
≈ 0.0000072%
❓ Frequently Asked Questions
What is probability?
Probability is a measure of the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain). A probability of 0.5 means there's a 50% chance.
How do you calculate probability?
Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes: P(A) = favorable outcomes / total outcomes.
What's the difference between probability and odds?
Probability is the ratio of favorable outcomes to total outcomes (e.g., 1/6). Odds are the ratio of favorable to unfavorable outcomes (e.g., 1:5).
What are independent events?
Independent events are events where the outcome of one doesn't affect the outcome of another. For example, each coin flip is independent of previous flips.
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Dr. Snezana Lawrence
Mathematical Historian | PhD from Yale
Dr. Lawrence is a published mathematical historian with a PhD from Yale University. She ensures mathematical precision and accuracy in all our calculations, conversions, and academic score calculators. Her expertise spans computational mathematics and educational assessment.
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