Probability Calculator

Probability is a measure of the likelihood that an event will occur. It is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. The formula is: P(A) = Number of favorable outcomes / Total number of possible outcomes. Probability values range from 0 (impossible event) to 1 (certain event).

Probability and odds are related but different concepts. Probability is the ratio of favorable outcomes to total outcomes, while odds are the ratio of favorable outcomes to unfavorable outcomes. For example, if the probability of an event is 1/6 (like rolling a specific number on a die), the odds would be 1:5 (1 favorable outcome to 5 unfavorable outcomes).

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads “the probability of A given B.” The formula is: P(A|B) = P(A and B) / P(B). This concept is fundamental in understanding how events relate to each other.

For independent events (events where the occurrence of one doesn’t affect the other), the probability of both occurring is the product of their individual probabilities: P(A and B) = P(A) × P(B). The probability of either occurring is: P(A or B) = P(A) + P(B) – P(A and B). These formulas are essential for calculating probabilities in scenarios with multiple independent events.

Complementary events are pairs of events where one is the exact opposite of the other. The sum of their probabilities is always 1. If event A has probability P(A), then its complement (not A) has probability 1 – P(A). For example, if the probability of rain tomorrow is 0.3, then the probability of no rain is 0.7.