ProbLab

Probability Calculator

Favorable outcomes over total outcomes — the foundation of probability.

Favorable outcomes (A)

Total possible outcomes

Favorable outcomes (B, optional)

P(A): 0.077
P(not A): 0.923
P(A and B): 0.019

What you entered

Favorable: 4Total: 52

1
P(A) = favorable ÷ total outcomes
4 ÷ 52= 0.0769
2
P(not A) = 1 − P(A)
1 − 0.0769= 0.9231
3
P(B) = favorable(B) ÷ total outcomes
13 ÷ 52= 0.25
4
P(A and B), assuming independence
0.0769 × 0.25= 0.0192

Result

P(A): 0.077

With 4 favorable outcomes out of 52 total, P(A) = 0.077 — about 7.7% likely.

Basic probability for common cases

Probability is favourable outcomes divided by total outcomes, assuming every outcome is equally likely. The complement is one minus that.

Favourable	Total	Probability	Probability not	Example
1	6	0.1667	0.8333	Rolling a specific number on a die
1	2	0.5000	0.5000	A coin landing heads
3	10	0.3000	0.7000	Drawing 1 of 3 winners from 10
1	52	0.0192	0.9808	Drawing one specific card
13	52	0.2500	0.7500	Drawing any heart
4	52	0.0769	0.9231	Drawing any ace

The complement column is often the easier route to an answer: the chance of at least one head in three coin tosses is fiddly to count directly, but is simply 1 minus the chance of no heads, which is 1 - 0.125 = 0.875. This formula assumes equally likely outcomes, which holds for fair dice and shuffled cards but not for most real situations - the probability of rain is not one over the number of weather types. For events in sequence, multiply probabilities when they are independent, and adjust the totals when they are not, as with drawing cards without replacement.

The simplest probability rule

P(A) is just favorable outcomes divided by total possible outcomes, assuming each outcome is equally likely — everything else in probability theory builds on this single ratio.

Combining independent events

When two events don't influence each other (like two separate coin flips), the probability of both happening is simply P(A) × P(B) — this calculator shows that multiplication step explicitly.

Frequently asked questions

I flip a coin 3 times. What's the probability of getting exactly 2 heads?

There are 8 total outcomes (2³). Exactly-2-heads outcomes: HHT, HTH, THH = 3. So P = 3/8 = 37.5%. For more complex versions of this question, use the binomial probability calculator.

What is the complement of a probability?

P(not A) = 1 − P(A). If there's a 30% chance of rain, there's a 70% chance of no rain. Complements are powerful for 'at least one' problems: P(at least one head in 5 flips) = 1 − P(no heads) = 1 − (0.5)⁵ = 96.875%.

How do I calculate the probability of A or B?

If A and B can't happen simultaneously (mutually exclusive): P(A or B) = P(A) + P(B). If they can overlap: P(A or B) = P(A) + P(B) − P(A and B). The subtraction prevents double-counting the overlap.

What is the difference between theoretical and experimental probability?

Theoretical: calculated from known outcomes (a fair die has P(6) = 1/6). Experimental: measured from actual trials (you rolled a 6 in 18 out of 100 rolls = 18%). They converge with enough trials — the law of large numbers.