Probability Calculator

Q: How do you calculate conditional probability P(A|B)?

Conditional probability P(A|B) represents the probability of event A happening given that event B has already occurred. It is calculated as P(A and B) / P(B).

Calculate probabilities for single events, two independent/dependent events, series of events, and normal distributions.

Single Event Probability

Enter the number of favorable outcomes and total possible outcomes, or probability P(A).

Probability P(A) [0 to 1 or %]:

— OR —

Number of Favorable Outcomes:

Total Number of Outcomes:

Two Events Probability

Enter probabilities for Event A and Event B to compute Union, Intersection, and Conditional probabilities.

Probability of Event A — P(A):

Probability of Event B — P(B):

P(A and B) / P(A ∩ B) (optional):

Series of Independent Events

Enter probabilities separated by commas (e.g., 0.5, 0.2, 0.8) to calculate combined AND / OR probabilities.

Probabilities (comma separated):

Normal Distribution Probability

Calculate Z-scores and area under the normal curve for given mean ($\mu$) and standard deviation ($\sigma$).

Mean ($\mu$):

Standard Deviation ($\sigma$):

Value $x_1$:

Value $x_2$ (optional for range):

Probability Formulas Summary

Probability of Event A: $P(A) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}$
Complement: $P(\text{not } A) = 1 - P(A)$
Union Rule (OR): $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
Intersection (Independent AND): $P(A \cap B) = P(A) \times P(B)$
Conditional Probability: $P(A|B) = \frac{P(A \cap B)}{P(B)}$

Frequently Asked Questions (FAQs)

Probability is a numerical measure ranging from 0 to 1 (or 0% to 100%) that indicates the likelihood of a specific event occurring.

Independent events are outcomes where one event occurring does not affect the likelihood of the other. Dependent events mean the outcome of one event alters the probability of the other.

Mutually exclusive events cannot happen at the exact same time. For mutually exclusive events A and B, $P(A \text{ and } B) = 0$.

Conditional probability $P(A|B)$ represents the probability of event A happening given that event B has already occurred. It is calculated as $\frac{P(A \cap B)}{P(B)}$.

Odds in favor of an event are the ratio of favorable outcomes to unfavorable outcomes, whereas probability is the ratio of favorable outcomes to total outcomes.