What is the difference between P(A and B) and P(A or B)?

P(A and B) is the probability both events occur simultaneously. P(A or B) is the probability at least one of them occurs. P(A or B) = P(A) + P(B) - P(A and B).

What does it mean for events to be independent?

Two events are independent if the outcome of one does not affect the probability of the other. This calculator assumes independence when computing P(A and B).

What is the complement of an event?

The complement of event A, written P(not A), is the probability that A does not occur. P(not A) = 1 - P(A). For example, if P(rain) = 0.3, then P(no rain) = 0.7.

Can probability be greater than 1?

No. Probability is always between 0 and 1 inclusive. A value of 0 means the event is impossible; 1 means it's certain.

What is the difference between theoretical and experimental probability?

Theoretical probability is calculated from known outcomes (like a fair coin). Experimental probability is based on observed results from actual trials and may differ from theoretical values.

Math

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Probability Calculator — Basic Advanced Probability

Calculate probability of single and multiple events. Find P(A), P(A or B), P(A and B), and complement probabilities.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

A probability calculator finds the likelihood of single and combined events occurring. It calculates P(A), P(not A), P(B), P(not B), P(A and B), and P(A or B) — expressed as both percentages and fractions. Probability ranges from 0 (impossible) to 1 (certain).

Favourable outcomes (Event A)

Total outcomes (Event A)

Favourable outcomes (Event B)

Total outcomes (Event B)

What is Probability Calculator — Basic Advanced Probability?

How to use it

1️⃣ Enter the number of favourable outcomes and total outcomes for Event A.
2️⃣ Optionally enter outcomes for Event B to calculate combined probabilities.
3️⃣ All results update instantly, showing each probability as both a percentage and a simplified fraction.
4️⃣ P(A and B) assumes the two events are independent.

Formula

P(A) = favourable outcomes / total outcomes. P(not A) = 1 - P(A). P(A and B) = P(A) × P(B) for independent events. P(A or B) = P(A) + P(B) - P(A and B).

💡 See it in action — a real example

Rolling a die: P(rolling a 3) = 1/6 ≈ 16.67%. Rolling two dice: P(both showing 3) = 1/6 × 1/6 = 1/36 ≈ 2.78%. P(at least one showing 3) = 1/6 + 1/6 - 1/36 = 11/36 ≈ 30.56%.

❓ Common questions

What is the difference between P(A and B) and P(A or B)?: P(A and B) is the probability both events occur simultaneously. P(A or B) is the probability at least one of them occurs. P(A or B) = P(A) + P(B) - P(A and B).
What does it mean for events to be independent?: Two events are independent if the outcome of one does not affect the probability of the other. This calculator assumes independence when computing P(A and B).
What is the complement of an event?: The complement of event A, written P(not A), is the probability that A does not occur. P(not A) = 1 - P(A). For example, if P(rain) = 0.3, then P(no rain) = 0.7.
Can probability be greater than 1?: No. Probability is always between 0 and 1 inclusive. A value of 0 means the event is impossible; 1 means it's certain.
What is the difference between theoretical and experimental probability?: Theoretical probability is calculated from known outcomes (like a fair coin). Experimental probability is based on observed results from actual trials and may differ from theoretical values.

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Percentage Calculator Mean Median Mode Calculator Standard Deviation Fraction Calculator