Probability Calculator
Calculate the probability of simple events, convert to percentage, and see odds.
Formula
P(A) = outcomes / total outcomes
Probability is the ratio of favorable outcomes to the total number of equally likely possible outcomes.
Worked Examples
Example 1: Coin Flip
Problem:Heads
Solution:1 success / 2 outcomes = 0.5
Result:50%
Example 2: Deck of Cards
Problem:Ace of Spades
Solution:1 card / 52 cards ≈ 0.019
Result:1.92%
Frequently Asked Questions
What is Probability?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain).
How do I convert Probability to Odds?
If Probability is P, Odds = P : (1-P). For example, if P=0.25, Odds are 0.25 : 0.75, which simplifies to 1:3.
Can probability be greater than 1?
No. Probability represents a portion of the total possibilities, so it is always between 0 and 1 (inclusive).
What are Independent Events?
Events where the outcome of one does not affect the other (e.g., rolling a die and flipping a coin).
What are Dependent Events?
Events where the outcome of the first affects the second (e.g., drawing cards from a deck without replacement).
What is the "Complement" of an event?
The complement of event A (denoted A') is the event that A does NOT occur. P(A') = 1 - P(A).
What is the "Law of Large Numbers"?
It states that as you perform more trials, the experimental probability will get closer and closer to the theoretical probability.
What does "Mutually Exclusive" mean?
Two events that cannot happen at the same time. For example, a single card cannot be both a King and a Queen.
How do I calculate probability of A AND B?
If independent: P(A and B) = P(A) × P(B). If dependent: P(A) × P(B|A).
Why must favorable and total outcomes come from the same sample space?
The formula P(A) = favorable / total only works when every outcome in the sample space is equally likely and each outcome is counted once. The sample space is the full list of possible results, such as the 6 faces of a fair die or the 52 cards in a deck. Mixing units — counting suits on top but cards on the bottom — breaks the ratio and gives a meaningless value.
Background & Theory
Probability (P):
A number between 0 and 1 measuring the likelihood of an event occurring.
- 0: Impossible event.
- 1: Certain event.
Formula:
P(A) = Number of favorable outcomes / Total number of possible outcomes
Odds:
Often expressed as "Successes : Failures".
If P(A) = 0.25 (1/4), the Odds are 1:3.