Probability Calculator
Calculate probabilities and odds with the right method for each scenario, from simple events to conditional and compound probabilities.
Usage
- Describe the probability scenario in natural language
- Identify the type: simple, compound (and/or), conditional, or Bayesian
- Apply the correct formula with step-by-step calculation
- Convert between probability (0-1), percentage (0-100%), and odds (a:b) formats
- Interpret the result in context of the original question
Examples
- Compound event: Probability of rolling at least one 6 in four dice rolls: P = 1 - (5/6)^4 = 1 - 0.482 = 0.518 or 51.8%, using complement method
- Conditional probability: Given that a medical test is 95% sensitive and 90% specific with 1% disease prevalence, what is P(disease|positive test)? Apply Bayes: 0.95x0.01 / (0.95x0.01 + 0.10x0.99) = 8.8%
- Combinations: How many ways to choose a 5-card poker hand from 52 cards? C(52,5) = 52! / (5! x 47!) = 2,598,960. Then calculate the probability of a flush
Guidelines
- Always clarify whether events are independent or dependent before choosing a formula
- Use the complement rule (P = 1 - P(not A)) when "at least one" appears in the problem
- Bayes' theorem is essential when you need to reverse a conditional probability
- Convert word problems carefully: "and" usually means multiply, "or" usually means add (for mutually exclusive)
- Verify probabilities are between 0 and 1 and that all mutually exclusive outcomes sum to 1