Probability Calculator
Your all-in-one tool to calculate probabilities for single and multiple events, with clear, step-by-step solutions.
Probability of a Single Event
Example Scenarios:
Probability of Two Independent Events
Practice Problems
Test your knowledge by solving the problem.
Probability Cheat Sheet & Concept Primer
Basic Probability
The likelihood of an event occurring, calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Formula: P(A) = Favorable / Total
Probability of A or B
The chance that either Event A or Event B (or both) will occur. For mutually exclusive events, it's just P(A) + P(B).
Formula: P(A or B) = P(A) + P(B) - P(A and B)
Probability of A and B
The chance that both Event A and Event B will occur. This formula applies if the events are independent.
Formula: P(A and B) = P(A) * P(B)
Complementary Events
The probability that an event does NOT occur is 1 minus the probability that it does occur.
Formula: P(not A) = 1 - P(A)
How to Solve Probability Problems: A Quick Tutorial
1. Identify the Event
First, clearly define the specific event you want to find the probability for. For example, "rolling a 4 on a standard six-sided die."
2. Count Favorable Outcomes
Determine how many ways the desired event can occur. In our example, there is only one way to roll a 4.
3. Count Total Outcomes
Count all the possible outcomes of the action. For a standard die, there are six possible outcomes (1, 2, 3, 4, 5, 6).
4. Calculate the Probability
Use the formula: P(Event) = Favorable / Total. For our example, the probability is 1 / 6, which is approximately 0.167 or 16.7%.
Frequently Asked Questions
What is probability?
Probability is a branch of mathematics that deals with the likelihood of events occurring. It is expressed as a number between 0 (impossible) and 1 (certain).
What are independent events?
Two events are independent if the outcome of one does not affect the outcome of the other. For example, flipping a coin twice are independent events.
What are mutually exclusive events?
Two events are mutually exclusive if they cannot both happen at the same time. For example, when rolling a single die, you cannot roll both a 3 and a 5 simultaneously.