Probability Calculator

Calculate AND, OR, NOT, and conditional probabilities

Event Probability

P(A) 30%
Formulas
P(NOT A) = 1 - P(A)
Odds = P(A) : P(NOT A)
Probability of A
30%
roughly 1 in 3.3
P(NOT A)
70%
1 in X
3.3
Odds For
3:7
Odds Against
7:3
Visual Comparison
Happens
30%
Doesn't
70%
Events are: Independent

Input Probabilities

P(A) 60%
P(B) 50%
P(A AND B)
30%
Probability both events occur
Venn Diagram
Probability Breakdown
P(A)
60%
P(B)
50%
P(A AND B)
30%
Events are: Not mutually exclusive

Input Probabilities

P(A) 40%
P(B) 30%
P(A AND B) 10%
P(A OR B)
60%
At least one event occurs
Venn Diagram
Probability Breakdown
P(A)
40%
P(B)
30%
P(A OR B)
60%

Conditional Probability

Calculate P(A|B) — the probability of A given B occurred.

P(A AND B) 15%
P(B) 40%
P(A | B)
37.5%
Probability of A given B occurred
How Conditioning Changes Probability
P(B) total
40%
P(A AND B)
15%
P(A | B)
37.5%

Example

If P(rain AND umbrella) = 15% and P(umbrella) = 40%, then P(rain | umbrella) = 15%/40% = 37.5%. Given someone has an umbrella, there's a 37.5% chance it's raining.

Bayes' Theorem

Update probability based on new evidence.

P(A) — Prior 1%
P(B|A) — Sensitivity 90%
P(B|NOT A) — False Positive 5%
P(A | B) — Posterior
15.4%
Probability of A after observing B
Prior vs Posterior
Prior P(A) 1%
Posterior P(A|B) 15.4%
P(NOT A | B) 84.6%
P(NOT A)
99%
P(B) Total
5.85%

Interpretation

Even with a 90% sensitive test, a positive result for a 1% prevalence condition only gives a 15.4% chance of truly having it. Most positives are false positives.

Probability Rules Reference

NOT Rule (Complement)

The probability of an event NOT occurring.

P(NOT A) = 1 - P(A)

AND Rule (Intersection)

Independent: One doesn't affect the other.

P(A AND B) = P(A) × P(B)

Dependent: One affects the other.

P(A AND B) = P(A) × P(B|A)

OR Rule (Union)

Mutually exclusive: Cannot both occur.

P(A OR B) = P(A) + P(B)

Not exclusive: Can both occur.

P(A OR B) = P(A) + P(B) - P(A AND B)

Bayes' Theorem

Update beliefs based on new evidence.

P(A|B) = P(B|A) × P(A) / P(B)

Where P(B) is the total probability:

P(B) = P(B|A)×P(A) + P(B|¬A)×P(¬A)

Privacy & Limitations

  • All calculations run entirely in your browser -- nothing is sent to any server.
  • Results are computed using standard formulas and should be verified for critical applications.

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Probability Calculator FAQ

What is Probability Calculator?

Probability Calculator is a free math tool that helps you Calculate probability for AND, OR, NOT, and conditional events.

How do I use Probability Calculator?

Enter your input values, review the calculated output, and adjust inputs until you reach the result you need. The result updates in your browser.

Is Probability Calculator private?

Yes. Calculations run locally in your browser. Inputs are not uploaded to a server by default, and refreshing the page clears session data.

Does Probability Calculator require an account or installation?

No. You can use this tool directly in your browser without sign-up or software installation.

How accurate are results from Probability Calculator?

This tool applies standard formulas or deterministic processing logic for estimates. For medical, legal, tax, or investment decisions, verify with a qualified professional.

Can I save or share outputs from Probability Calculator?

You can bookmark this page and copy outputs manually. Results are not persisted in your account and are typically not embedded in the URL.

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