Probability Solver
Master the math of chance. Calculate independent and joint probabilities instantly with our interactive event engine.
Event Odds
Decimal
0.50
Odds For
1.00:1
Decimal
0.50
Odds For
1.00:1
Calculations assume events A and B are **independent**. This means the occurrence of one does not affect the probability of the other.
P(A and B)
Both events happen
25.00%
P(A or B)
At least one happens
75.00%
P(Not A)
Event A does not happen
50%
P(Neither)
Neither event happens
25.00%
Set Intersection Analysis
Visualizing the relative likelihood of A vs B
Fundamental Rules
Probability measures the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain).
Core Formulas
- Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
- Multiplication Rule: P(A and B) = P(A) × P(B)
- Complement Rule: P(Not A) = 1 - P(A)
- Odds For: P(A) / P(Not A)
Real-World Usage
Risk Assessment
Insurance companies use it to price premiums based on event likelihood.
Finance
Predicting stock market movements and portfolio risk management.
Medicine
Calculating the effectiveness of treatments and diagnostic accuracy.
Gambling & Games
Understanding the house edge and expected value (EV).
Fun Fact
"If you flip a coin 10 times and get heads every time, the probability of the 11th flip being heads is still exactly 50%."
Independent vs. Dependent
The relationship between events changes how we calculate the odds.
Independent
The outcome of Event A has NO impact on Event B.
Dependent
The outcome of Event A DOES impact Event B.