What is the Probability Calculator?
The Probability Calculator is an essential statistical tool designed to help students, researchers, and professionals quickly evaluate the likelihood of different events. Whether you are dealing with basic independent occurrences, trying to solve missing variables in complex event scenarios, calculating the probability of a series, or finding the area under a normal distribution curve, this calculator provides precise and instant results.
Probability is fundamentally the measure of the likelihood that an event will occur. It is quantified as a number between 0 and 1, with 1 signifying absolute certainty, and 0 signifying that the event cannot possibly occur. The higher the probability, the more certain it is that the event will happen.
How to Use This Calculator
To get started, select your required operation from the Calculator Type dropdown menu. Based on your selection, specific input fields will appear on the left panel.
- Two Independent Events: Enter the probabilities of Event A and Event B to instantly find intersections, unions, and exclusive events.
- Two Events Solver: If you only have partial data (e.g., you know P(A) and P(A ∪ B)), simply input those two values and the solver will automatically deduce the remaining statistics.
- Series of Independent Events: Calculate the chance of Event A happening multiple times in a row, followed by Event B.
- Normal Distribution: Enter the mean, standard deviation, and your bounds (left and right). Use
infor-inffor infinite bounds.
The Formula / The Method / The Science
When working with two independent events, the outcomes of one do not affect the other. Our calculator uses foundational statistical formulas to derive the results.
Complement of an Event (A')
The complement represents the probability that the event does not occur.
Example: If the probability of rain is 0.30, the probability of no rain is 1 - 0.30 = 0.70.
Intersection of A and B (A ∩ B)
The intersection is the probability that both events occur simultaneously. For independent events, we multiply them.
Example: Rolling a 6 on a die twice: (1/6) × (1/6) = 1/36 ≈ 0.0278.
Union of A and B (A ∪ B)
The union calculates the likelihood that either Event A, Event B, or both occur.
Frequently Asked Questions
Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. For example, flipping a coin and rolling a die are independent events; getting a 'heads' doesn't change the odds of rolling a '6'.
Mutually exclusive means two events cannot happen at the same time (e.g., drawing a single card that is both a Heart and a Spade is impossible). Independent means the events can happen at the same time, but one doesn't influence the other.
If you want to calculate the probability of a value being strictly greater than a number (meaning no upper limit), enter inf in the Right Bound field. For strictly less than a number, enter -inf in the Left Bound field.
The Two Events Solver uses an algebraic iteration process. If you know that two events are independent and you provide any two valid statistical metrics (for example, P(A) and P(A ∪ B)), the solver algorithm works backward using foundational probability formulas to fill out the remaining six metrics automatically.
No. By definition, a probability is a quantifiable measure of likelihood expressed strictly as a number between 0 and 1 (or 0% and 100%). A probability of 0 means the event is impossible, while a probability of 1 means the event is absolutely guaranteed to occur.