Probability Calculator

Calculate probabilities for various scenarios using different probability models

Calculation Type:

Favorable Outcomes: Number of ways the event can occur

Total Possible Outcomes: Total number of possible outcomes

Event 1 Probability:

Event 2 Probability:

Events are independent (don't influence each other)

Calculate the probability of achieving exactly, at least, or at most k successes in n trials

Number of Trials (n):

Probability of Success in One Trial (p):

Number of Successes (k):

Calculation Type:

Calculation Type: Combination example: lottery numbers (5,12,23,45,48 is the same as 48,45,23,12,5)
Permutation example: lock combination (1-2-3 is different from 3-2-1)

Total Items (n): Total number of items to choose from (e.g., 52 cards in a deck)

Items Chosen (r): Number of items you're selecting (e.g., 5 cards for a poker hand)

Allow repetition (items can be chosen more than once)

Calculate P(A|B) using Bayes' Theorem:

P(A) - Prior Probability: The probability of event A occurring (before considering event B)

P(B|A) - Likelihood: The probability of event B occurring given that A has occurred

P(B|not A) - False Positive Rate: The probability of event B occurring given that A has not occurred

Understanding Probability

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. The higher the probability of an event, the more likely it is to occur.

Types of Probability Calculations

Our calculator supports several types of probability calculations:

Basic Probability

The probability of an event A is the number of favorable outcomes divided by the total number of possible outcomes:

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

Conditional Probability

The probability of an event A occurring given that another event B has already occurred:

P(A|B) = P(A and B) / P(B)

Binomial Probability

The probability of achieving exactly k successes in n independent trials, each with a probability p of success:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Combinations and Permutations

Combinations (order doesn't matter):

C(n,r) = n! / (r! × (n-r)!)

Permutations (order matters):

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

Bayes' Theorem

A formula to calculate conditional probability by incorporating prior knowledge:

P(A|B) = [P(B|A) × P(A)] / P(B)

Real-World Applications of Probability

Risk Assessment: Insurance companies use probability to calculate premiums
Medical Diagnosis: Doctors use conditional probability to interpret test results
Quality Control: Manufacturers use probability to test product reliability
Weather Forecasting: Meteorologists use probability to predict weather events
Gambling and Games: Casinos and game designers use probability to set odds
Machine Learning: AI systems use probability to make predictions

Understanding probability helps us make better decisions in uncertain situations, evaluate risks, and understand the likelihood of different outcomes.

Probability Calculator