Probability Calculator
Calculate classical event probability ($P(A) = \frac{n(A)}{n(S)}$), complement probability ($P(A')$), percentage %, and odds ratios.
Calculate Classical Event Probability
Enter number of favorable outcomes n(A) and total possible outcomes n(S).
Calculation Results
Calculated using classical Laplace probability equations: P(A) = \frac{n(A)}{n(S)}, \quad P(A') = 1 - P(A)
Quick Summary
The Probability Calculator evaluates classical event probability ($P(A) = \frac{n(A)}{n(S)}$), complement $P(A')$, percentage %, and odds ratios.
Formula Explanation
P(A) = \frac{\text{Number of Favorable Outcomes } n(A)}{\text{Total Possible Outcomes } n(S)}
P(A') = 1 - P(A)How It Works
Classical probability measures the likelihood of an event occurring when all outcomes in sample space $n(S)$ are equally likely. The Probability Calculator divides favorable outcomes $n(A)$ by total sample space $n(S)$, computing percentage likelihood and odds.
Step-by-Step Worked Example
Practical Problem: Rolling a fair 6-sided die, calculate the probability of rolling a 6 ($n(A) = 1, n(S) = 6$).
- Step 1: Identify favorable outcomes $n(A)$: Rolling a 6 $\rightarrow n(A) = \mathbf{1}$.
- Step 2: Identify total possible outcomes $n(S)$: 6 sides $\{1, 2, 3, 4, 5, 6\} \rightarrow n(S) = \mathbf{6}$.
- Step 3: Divide favorable outcomes by total: $P(A) = 1 / 6 = \mathbf{0.166667}$.
- Step 4: Calculate Complement Probability $P(A')$: $P(A') = 1 - 0.166667 = \mathbf{0.833333\text{ (83.33\%)}}.$
- Step 5: Express as Odds Ratio: Odds For $= 1 : 5$; Odds Against $= 5 : 1$.
Real-World Calculation Examples
Scenario 1: Rolling a 6 on a Die (1 in 6)
Parameters: n(A) = 1, n(S) = 6
Result: P(A) = 0.1667 (16.67% probability).
Scenario 2: Drawing an Ace from a Card Deck
Parameters: n(A) = 4 aces, n(S) = 52 cards
Result: P(A) = 0.0769 (7.69% probability).
Scenario 3: Flipping Heads on a Coin
Parameters: n(A) = 1, n(S) = 2
Result: P(A) = 0.5000 (50.00% probability).
Scenario 4: Winning a 100-Ticket Raffle
Parameters: n(A) = 5 tickets held, n(S) = 100 tickets
Result: P(A) = 0.0500 (5.00% probability).
Key Benefits of Using This Calculator
Event & Complement Calculation
Outputs event probability $P(A)$ and complement $P(A')$ simultaneously.
Odds Ratio Conversion
Converts classical probability into odds for ($a:b$) and odds against ($b:a$).
Multi-Format Representation
Displays probabilities as decimals, percentages, and fractions.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is classical probability?
Classical probability is the ratio of favorable outcomes to total possible outcomes when all outcomes are equally likely.
What is Law of Large Numbers (LLN)?
LLN states that as the number of experimental repetitions increases, empirical relative frequency converges to theoretical probability.
What is complement rule $P(A')$?
The complement rule states that the probability of an event NOT happening is $1 - P(A)$.
What are Kolmogorov's Axioms of Probability?
1. $0 \le P(A) \le 1$. 2. $P(S) = 1$. 3. For mutually exclusive events, $P(A \cup B) = P(A) + P(B)$.
Can probability be greater than 1 or negative?
No — probability is strictly bounded between $0.0$ (0%) and $1.0$ (100%).
What is subjective probability?
Subjective probability reflects personal belief or expert judgment when historical frequency data is unavailable.
How do I calculate probability in Excel?
Use division formula =favorable / total or PROB function.
What is difference between odds and probability?
Probability compares favorable outcomes to total outcomes ($\frac{a}{a+b}$); odds compare favorable outcomes to unfavorable outcomes ($\frac{a}{b}$).
What is sample space $S$?
Sample space $S$ is the set of all possible outcomes of a random experiment.
What are mutually exclusive events?
Mutually exclusive events cannot happen at the same time ($P(A \cap B) = 0$).