What does the Probability Calculator do?

Calculate event probabilities, combinations and permutations. P(A or B), P(A and B), nCr, nPr. All calculations are performed in your browser using official UK rates and thresholds.

How accurate are the results?

This calculator uses standard mathematical algorithms and provides results accurate to the precision shown. For very large numbers or high-precision requirements, results are rounded to a reasonable number of decimal places.

Can I use this for schoolwork?

Yes. This calculator is suitable for GCSE, A-level and university-level mathematics. It follows standard mathematical conventions used in UK education.

Probability Calculator

Calculate event probabilities, combinations and permutations. P(A or B), P(A and B), nCr, nPr.

Last updated: April 2026 · Source: BBC Bitesize — Probability

Event Probability

P(A)

P(B)

P(A or B)

0.6500

P(A and B)

0.1500

P(not A)

0.7000

P(A|B)

0.3000

Assumes independent events. P(A or B) = P(A) + P(B) - P(A)P(B)

Combinations & Permutations

n (total items)

r (choosing)

C(n,r) Combinations

120

Order doesn't matter

P(n,r) Permutations

720

Order matters

Disclaimer

This calculator is provided for informational purposes only and should not be considered as financial or tax advice. All calculations are performed locally in your browser — no personal data is collected or sent to our servers. Rates and thresholds are sourced from HMRC and GOV.UK and are updated for the current tax year. Always verify results with HMRC or consult a qualified professional before making financial decisions.

How It Works

Probability measures the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). This calculator handles simple probability, compound events (AND/OR), conditional probability and permutations and combinations.

For independent events, the probability of A AND B is P(A) × P(B). For mutually exclusive events, the probability of A OR B is P(A) + P(B). For non-mutually exclusive events, P(A OR B) = P(A) + P(B) − P(A AND B). The calculator selects the correct formula based on your inputs.

Combinations (nCr) count selections where order does not matter, such as lottery draws. Permutations (nPr) count arrangements where order matters. The calculator computes both using the factorial formula and displays results as a whole number and as a probability.

Example: Probability of drawing two red cards from a deck

Red cards in a standard deck: 26 out of 52
First draw: 26/52 = 1/2
Second draw (without replacement): 25/51
Combined: 1/2 × 25/51 = 25/102 ≈ 0.245 (24.5%)

Source: BBC Bitesize — Probability

Frequently Asked Questions

What does the Probability Calculator do?: Calculate event probabilities, combinations and permutations. P(A or B), P(A and B), nCr, nPr. All calculations are performed in your browser using official UK rates and thresholds.
How accurate are the results?: This calculator uses standard mathematical algorithms and provides results accurate to the precision shown. For very large numbers or high-precision requirements, results are rounded to a reasonable number of decimal places.
Can I use this for schoolwork?: Yes. This calculator is suitable for GCSE, A-level and university-level mathematics. It follows standard mathematical conventions used in UK education.