Understanding Probability
Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Understanding probability is fundamental to decision-making under uncertainty — from weather forecasting and medical diagnosis to gambling odds and insurance pricing. Basic probability divides the number of favourable outcomes by the total number of possible outcomes.
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Formula
Probability Calculator
Calculate probability of an event and its complement from outcomes.
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Worked Example
Given:
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FAQs
What is the complement of a probability?
The complement of an event A is the probability that A does not occur: P(not A) = 1 - P(A). If there is a 30% chance of rain, there is a 70% chance of no rain. The complement rule is useful for calculating the probability of 'at least one' event: P(at least one) = 1 - P(none).
What is the difference between probability and odds?
Probability is expressed as a fraction of total outcomes: 1/4 means 1 in 4 chance. Odds compare favourable to unfavourable outcomes: odds of 1:3 means 1 favourable for every 3 unfavourable. To convert probability to odds: if P = 1/4, odds = 1:(4-1) = 1:3.
What are independent vs dependent events?
Independent events do not affect each other's probability — flipping a coin twice. Dependent events influence each other — drawing cards without replacement. For independent events: P(A and B) = P(A) × P(B). For dependent events: P(A and B) = P(A) × P(B|A) where P(B|A) is the conditional probability of B given A.