Probability Calculator: How to Calculate Probability for Any Event

Probability tells you how likely something is to happen. From weather forecasts to sports betting to medical testing — understanding probability helps you make better decisions.

The basic formula

P(Event) = Favourable outcomes ÷ Total possible outcomes

Example: Rolling a 3 on a standard die: P(3) = 1 ÷ 6 = 0.167 = 16.7%

Combined events

P(A AND B) — Both events happening

• Independent events: P(A and B) = P(A) × P(B)
  • Rolling two 6s: 1/6 × 1/6 = 1/36
• Dependent events: P(A and B) = P(A) × P(B|A)

P(A OR B) — Either event happening

• Mutually exclusive: P(A or B) = P(A) + P(B)
  • Rolling a 2 or 5: 1/6 + 1/6 = 2/6
• Not exclusive: P(A or B) = P(A) + P(B) − P(A and B)

Binomial distribution

When you repeat an experiment n times with success probability p:

P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Example: Probability of exactly 3 heads in 5 coin flips: P = C(5,3) × 0.5³ × 0.5² = 10 × 0.125 × 0.25 = 0.3125 (31.25%)

Conditional probability (Bayes’ theorem)

“What’s the probability of A given that B has already happened?”

P(A|B) = P(B|A) × P(A) ÷ P(B)

Real example: A medical test is 99% accurate. The disease affects 1 in 1000 people. If you test positive, what’s the actual probability you have it?

P(Disease|Positive) = (0.99 × 0.001) ÷ (0.99 × 0.001 + 0.01 × 0.999) = 0.09 = 9%

Even with a 99% accurate test, a positive result only means 9% probability — because the disease is so rare.

Quick reference

Probability	Meaning
0	Impossible
0.01	Very unlikely
0.25	Unlikely
0.50	Even chance
0.75	Likely
0.99	Almost certain
1	Certain

Calculate any probability with our Probability Calculator — supports basic, binomial, and conditional probability with full formulas shown.