Probability Calculator
Show the math
What Your Result Means
- P(A) — Probability: A decimal between 0 and 1 representing the chance the event occurs. A value of 0 means impossible; 1 means certain.
- P(not A) — Complement: The chance the event does NOT occur. Always equals 1 minus P(A).
- P(A and B): For independent events, the probability both occur. Computed by multiplying P(A) × P(B). This number gets small quickly as you add more events.
- P(A or B): The probability that at least one of the two events occurs. Always greater than or equal to either individual probability alone.
- Coin Flip Probability: Uses the binomial formula to find the exact chance of getting a specific number of heads in a given number of flips, assuming a fair coin (50/50).
How This Calculator Works
For a single event, you enter favorable and total outcomes; the tool divides to get P(A) and subtracts from 1 for the complement. For two independent events, it multiplies probabilities for "and," adds them minus the overlap for "or," and divides for the conditional. The coin flip tab uses the binomial coefficient C(n, k) × 0.5ⁿ to compute the exact probability. All tabs assume events are independent — dependent events require conditional probability adjustments not covered here.
Quick Questions
What does "independent" mean for two events?
Two events are independent if the outcome of one doesn't affect the other. Flipping two coins is independent — the first flip doesn't change the odds of the second. Drawing cards without replacement is dependent because the deck changes after each draw.
Why does P(A or B) subtract P(A and B)?
Without the subtraction, you'd double-count outcomes where both events happen. The inclusion-exclusion formula P(A or B) = P(A) + P(B) − P(A and B) corrects for this overlap.
Is this a fair coin assumption?
Yes. The coin flip tab assumes exactly 50% heads and 50% tails on each flip. For a biased coin, you'd need a generalized binomial formula with a different probability parameter.
What's the maximum number of flips supported?
The calculator uses JavaScript's built-in number precision, which limits accuracy for factorials beyond about 170. For typical use (under 50 flips), results are exact. Very large values may lose precision.
Sources
- Khan Academy — Probability (probability fundamentals and formulas)
- Wikipedia — Binomial Distribution (coin flip / binomial formula)
- Stat Trek — Probability Rules (addition and multiplication rules)
Method & review
Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.