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Basic Probability Calculator

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Basic Probability Calculator

Probability turns a guess into a real number. This tool covers five common situations. Pick the one that matches your question below.

Single Event
A and B
A or B
Complement (Not A)
A given B
P(A) = Favorable outcomes ÷ Total outcomes
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A and B)
P(not A) = 100% − P(A)
P(A given B) = P(A and B) ÷ P(B)
Your probability 0%
Chance it happens: 0%
Chance it does not: 0%
How likely is this, in plain terms?
Very unlikelyEven chanceVery likely

What probability really means

Probability is just a way to measure how likely something is. It always sits between 0 percent and 100 percent.

A 0 percent chance means something cannot happen. A 100 percent chance means it always happens.

Everything else falls somewhere in between, and this tool helps you find that exact number.

Single Event: how likely is one outcome?

P(A) = Favorable outcomes ÷ Total outcomes

Favorable outcomes are the results you actually want. Total outcomes are everything that could possibly happen.

Everyday example: a bag has 3 red balls and 7 blue balls, 10 balls in total. Picking a red ball has 3 favorable outcomes out of 10. That gives a 30 percent chance.
Why calculate this: use it any time you want your real chances before something happens.

A and B: what are the odds both things happen?

P(A and B) = P(A) × P(B)

Multiply both chances together. This only works when one event does not affect the other.

Everyday example: chance of rain today is 40 percent. Chance your bus arrives late is 25 percent. Both happening together is 10 percent.
Why calculate this: it helps you plan for two problems hitting you at the same time.

A or B: what are the odds at least one thing happens?

P(A or B) = P(A) + P(B) − P(A and B)

Add both chances together, then remove the overlap so it is not counted twice.

Everyday example: chance of rain is 30 percent, chance of a delayed flight is 20 percent. Facing at least one problem comes to 44 percent.
Why calculate this: it shows your total exposure when more than one thing could go wrong.

Complement: what are the odds it does not happen?

P(not A) = 100% − P(A)

Subtract the chance of something happening from 100 percent.

Everyday example: if rain has a 30 percent chance, staying dry has a 70 percent chance instead.
Why calculate this: planning around what will not happen is sometimes the easier path.

A given B: how does new information change the odds?

P(A given B) = P(A and B) ÷ P(B)

This finds the chance of A once you already know that B has happened.

Everyday example: a weather app shows rain on 12 percent of all days, and clouds on 40 percent of days. If it is cloudy today, your updated chance of rain becomes 30 percent.
Why calculate this: real decisions usually depend on information you already have, not a blind guess.

Frequently asked questions

What is the difference between theoretical and experimental probability?

Theoretical probability comes from a formula. Experimental probability comes from testing something many times and counting the actual results.

Can probability be negative?

No. Probability always stays between 0 percent and 100 percent, with nothing outside that range.

Does a high probability guarantee something will happen?

No. Even a 95 percent chance still leaves real room for the unlikely outcome to occur.

What does independent mean in probability?

Independent events do not affect each other. One event happening changes nothing about the other one.

Why do people confuse probability with statistics?

Probability predicts what might happen next. Statistics studies what already happened and draws conclusions from it.

Curious how likelihood connects to real financial risk?

See how probability thinking applies to investing.

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