Probability Calculator
Calculate the probability of single or multiple independent events with step-by-step solutions using our free online probability calculator.
How to Use This Calculator
- Select either Single Event or Multiple Events mode.
- Single Event: Enter the number of favorable outcomes and total possible outcomes.
- Multiple Events: Enter the probability of a single event (0 to 1) and the number of independent trials.
- Click Calculate Probability to see the result with step-by-step explanation.
Formulas
Multiple Events (independent):
P(all succeed) = P(E)n
P(none succeed) = (1 − P(E))n
P(at least one) = 1 − (1 − P(E))n
These formulas apply to independent events where the outcome of one does not affect the others.
Examples
Coin Toss
Probability of heads = 1/2 = 0.5 (50%). Getting 3 heads in a row = 0.5³ = 0.125 (12.5%).
Dice Roll
Rolling a 6 on a fair die = 1/6 ≈ 0.1667 (16.67%). Rolling at least one 6 in 4 tries = 1 − (5/6)&sup4; ≈ 51.77%.
Deck of Cards
Drawing an Ace = 4/52 ≈ 0.0769 (7.69%). Drawing a heart = 13/52 = 0.25 (25%).
Frequently Asked Questions
What is the range of probability?
Probability ranges from 0 (impossible) to 1 (certain). It is often expressed as a percentage (0% to 100%).
What are independent events?
Events are independent if the outcome of one does not affect the other. Coin flips and dice rolls are classic examples.
How do I calculate the probability of A and B?
For independent events: P(A and B) = P(A) × P(B). For dependent events: P(A and B) = P(A) × P(B|A).
What are odds?
Odds compare the probability of an event happening to it not happening. Odds = P / (1 − P).