Probability Calculator

Calculate probabilities of single and multiple events with our advanced, easy-to-use probability tool. Perfect for statistics, games, and risk assessment.

Single Event Probability Calculator

Calculate the probability of a single event occurring. Enter the number of favorable outcomes and total possible outcomes.

Probability: 16.67% (1 in 6)
Formula:

P(A) = Number of favorable outcomes / Total number of possible outcomes

Multiple Events Probability Calculator

Calculate the probability of multiple events occurring. Choose between independent or dependent events.

Probability: 25.00% (Both events occurring)
Formulas:

Independent P(A AND B) = P(A) × P(B)

Independent P(A OR B) = P(A) + P(B) - P(A) × P(B)

Dependent P(A AND B) = P(A) × P(B|A)

Combinations & Permutations Calculator

Calculate the number of possible combinations or permutations. Combinations don't consider order, while permutations do.

Combinations: 120
Formulas:

Combination: C(n,k) = n! / (k! × (n-k)!)

Permutation: P(n,k) = n! / (n-k)!

Combination with repetition: (n+k-1)! / (k! × (n-1)!)

Conditional Probability Calculator

Calculate the probability of an event occurring given that another event has already occurred.

P(A|B) = 50.00%
Formula:

P(A|B) = P(A ∩ B) / P(B)

Understanding Probability Calculations

What is Probability?

Probability is a measure of the likelihood that an event will occur. It's quantified as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. In everyday terms, probability is often expressed as a percentage between 0% and 100%.

Key Probability Concepts

  • Single Event Probability: The chance of one specific outcome occurring (e.g., rolling a 3 on a die).
  • Multiple Events: Calculating probabilities when more than one event is involved, considering whether events are independent or dependent.
  • Combinations & Permutations: Counting possible arrangements where order matters (permutations) or doesn't matter (combinations).
  • Conditional Probability: The probability of an event occurring given that another event has already occurred.

Real-World Applications

Probability calculations are essential in many fields:

  • Statistics: For data analysis and interpretation
  • Finance: Risk assessment and investment strategies
  • Science: Experimental design and result analysis
  • Gaming: Calculating odds and designing fair games
  • Weather Forecasting: Predicting chance of precipitation

How Our Probability Calculator Helps

Our advanced probability calculator simplifies complex probability calculations, providing accurate results instantly. Whether you're a student learning probability concepts, a researcher analyzing data, or just curious about the odds, this tool makes probability calculations accessible to everyone.