Probability Calculator

Calculate probability of events, combinations, permutations, and statistical analysis with our advanced probability calculator. Get instant accurate results for all your probability calculations.

How It Works

Follow these simple steps to calculate probability accurately:

1

Select Calculation Type

Choose whether you want to compute a basic probability, combination, or permutation depending on whether order matters.

2

Enter Your Values

Input total possible outcomes, number of favorable events, or selection values (n and r).

3

Get Results

Click Calculate to see results instantly, complete with formulas, intermediate steps, and interpretation.

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Understanding the Tools

Understanding Probability

Probability measures the likelihood that an event will occur, expressed between 0 and 1:

  • 0 means impossible (event cannot occur).
  • 1 means certain (event will definitely occur).
  • 0.5 means an even chance (like flipping a fair coin).
  • Values between 0 and 1 represent varying levels of likelihood.
  • Mixed Numbers: means equal chance (like flipping a fair coin).

Basic Probability Formula

P(Event) = Number of Favorable Outcomes / Total Number of Outcomes

P(3) = 1/6 ≈ 0.1667 (16.67%)

Combinations (Order Doesn’t Matter)

C(n, r) = n! / (r!(n - r)!)

Example:

Selecting 2 cards from a 5-card deck:

C(5, 2) = 10 possible combinations.

Conditional Probability

Conditional probability determines the likelihood of an event A occurring given that another event B has already occurred.

P(A|B) = P(A ∩ B) / P(B)

Example:

If 40% of people like coffee, and 25% like both coffee and tea:

P(Tea | Coffee) = 0.25 / 0.40 = 0.625 (62.5%)

Permutations (Order Matters)

P(n, r) = n! / (n - r)!

Example:

Arranging 3 medals among 5 athletes:

P(5, 3) = 60 possible outcomes.

Interpreting Probability Values

Probability Range
Meaning
Example
0
Impossible
Drawing a 13 from a deck of 52 cards
0.25
Unlikely
Rain on a dry summer day
0.5
Even chance
Heads or tails on a fair coin
0.75
Likely
Drawing a red card from a standard deck
1
Certain
Drawing any card from the deck

Common Real-World Applications

  • • Games & Lottery – Calculate odds of winning draws or dice rolls
  • • Finance & Risk – Estimate market or investment risks
  • • Science & Research – Predict outcomes in experiments
  • • Sports Analytics – Forecast player or team performance
  • • Medical Studies – Assess likelihood of health outcomes

Frequently Asked Questions

Get answers to common questions about probability calculations

Combinations ignore order, while permutations consider order.

Use the formula P(A|B) = P(A ∩ B) ÷ P(B).

It’s the ratio of possible favorable outcomes to all possible outcomes under ideal conditions.

No. Probability always ranges from 0 (impossible) to 1 (certain). .

There are 3 even numbers (2, 4, 6), so P = 3/6 = 0.5 or 50%.

P(A ∩ B) = P(A) × P(B).

P(A ∩ B) = P(A) × P(B|A).

Yes. You can compute probability for single, dependent, or independent multiple events.

Use the combination formula: Odds = 1 ÷ C(n, r), where n = total numbers and r = numbers drawn.