Probability Calculator — Step-by-Step Solutions

The Probability Calculator helps you determine the likelihood of events. Calculate single event probability, complementary probability, and combined probabilities using union and intersection rules.

Enter the number of favourable outcomes and total possible outcomes to find the probability. The calculator displays results as fractions, decimals, and percentages.

Favourable Outcomes

Total Outcomes

Result

—

Your calculations will appear here

How to Use the Probability Calculator

Enter the number of favourable outcomes and the total number of possible outcomes.
The calculator displays the probability as a fraction, decimal, and percentage.
It also shows the complementary probability (the chance the event does NOT occur).

Formula and Theory

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). The basic formula is P(A) = number of favourable outcomes / total number of possible outcomes.

Key rules: the complement rule states P(not A) = 1 - P(A). The addition rule for mutually exclusive events is P(A or B) = P(A) + P(B). For independent events, P(A and B) = P(A) * P(B).

Worked Examples

Example 1: Rolling a die

Problem: What is the probability of rolling a 4 on a fair six-sided die?

Solution: Favourable: 1 (just the number 4). Total: 6 sides.

Answer: P = 1/6 = 0.1667 = 16.67%

Example 2: Drawing a card

Problem: What is the probability of drawing a heart from a standard deck?

Solution: Favourable: 13 hearts. Total: 52 cards.

Answer: P = 13/52 = 1/4 = 25%

Example 3: Complement

Problem: If the probability of rain is 30%, what is the probability of no rain?

Solution: P(no rain) = 1 - P(rain) = 1 - 0.30

Answer: 70%

Frequently Asked Questions

What is the difference between theoretical and experimental probability?

Theoretical probability is calculated from known possible outcomes. Experimental probability is determined by running trials and counting how often an event occurs.

What does "independent events" mean?

Two events are independent if the outcome of one does not affect the outcome of the other. For example, flipping a coin twice: each flip is independent.

Can probability be greater than 1?

No. Probability ranges from 0 (impossible) to 1 (certain). A value greater than 1 indicates an error in the calculation.