Probability Calculator
Compute the probability of events, combinations, and permutations.
Probability of a Single Event
Combinations (nCr)
Permutations (nPr)
Understanding Probability and Combinatorics
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur. Combinatorics deals with counting, arrangement, and combination of objects.
Key Formulas:
- Probability of an Event: P(E) = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
- Combinations (nCr): C(n, r) = n! / [r! (n - r)!]
- Permutations (nPr): P(n, r) = n! / (n - r)!
Where '!' denotes factorial (e.g., 5! = 5 × 4 × 3 × 2 × 1).
Probability Examples
| Scenario | Calculation | Result |
|---|---|---|
| Rolling a 3 on a 6-sided die | 1/6 | 0.1667 |
| Choosing 2 items from 5 (order doesn't matter) | C(5, 2) = 5! / (2! * 3!) | 10 |
| Arranging 3 letters from ABC (order matters) | P(3, 3) = 3! / (3-3)! | 6 |
Frequently Asked Questions
What is probability?
Probability is a measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
What is the difference between permutations and combinations?
Permutations are arrangements where the order of selection matters (e.g., ABC is different from ACB). Combinations are selections where the order does not matter (e.g., {A, B, C} is the same as {C, B, A}).
How are probabilities used in real life?
Probabilities are used in various real-life scenarios, including weather forecasting, risk assessment in finance and insurance, medical diagnostics, quality control in manufacturing, and game theory.