Probability Calculator – Event Probability and Odds
Calculate probability, odds, and combined event probability for any scenario.
About This Calculator
Calculate probability, odds, and combined event probability for any scenario. Use the calculator above for instant results.
Probability, Odds, and Repeated Trials
For equally likely outcomes, event probability is the number of favorable outcomes divided by the total number of possible outcomes. Probability ranges from 0 to 1, or equivalently from 0% to 100%. A probability of 0 means impossible under the model; a probability of 1 means certain.
Odds and probability describe the same situation in different forms. If an event has f favorable outcomes and u unfavorable outcomes, odds in favor are f:u, while probability is f/(f+u). For a fair die, rolling a six has probability 1/6 and odds in favor of 1:5.
Repeated-trial calculations need an independence assumption when powers of a single probability are used. If each trial has the same event probability p and trials are independent, the probability that the event occurs on every one of n trials is pn. The probability that it occurs at least once is easier to compute through the complement: 1 − (1 − p)n.
Do not apply these formulas automatically to dependent events. Drawing cards without replacement changes the deck after each draw, so the probability on later draws is different. In that setting, conditional probability or combinations may be required.
Worked Examples
- P = 16.67% | Odds: 1:5
Answer: 16.67%
- P = 50% | Odds: 1:1
Answer: 50%
- P each = 50% | P(3 in a row) = 12.5%
Answer: 12.5%
For one fair die roll, p = 1/6 and failure probability is 5/6.
- P(at least one six) = 1 − (5/6)4
Answer: about 51.77%
Using the complement avoids separately adding the cases with one, two, three, and four sixes.
There are 4 aces among 52 cards.
- P(ace) = 4/52 = 1/13
Answer: about 7.69%
The fraction should be reduced only after the favorable and total outcomes are identified correctly.
Who Uses This Calculator?
Calculate odds and house edge.
Probability homework.
Experimental probability.
Business scenario probability.
Common Mistakes to Avoid
❌ Independent vs dependent events
Coin flips are independent. Drawing cards without replacement is dependent.
❌ Probability vs odds
Probability: favorable/total (0-1). Odds: favorable:unfavorable.
❌ Multiplying probabilities for dependent events as if they were independent
Without replacement, later probabilities change. For two aces drawn from a deck without replacement, use 4/52 × 3/51, not (4/52)2.
❌ Adding overlapping event probabilities without subtracting the overlap
For events that can occur together, P(A or B) = P(A) + P(B) − P(A and B). Omitting the overlap counts those outcomes twice.
Frequently Asked Questions
What is probability?
0 to 1 expressing likelihood. 0=impossible, 1=certain, 0.5=50/50.
Addition rule?
P(A or B) = P(A) + P(B) - P(A and B).
Multiplication rule?
Independent events: P(A and B) = P(A) x P(B).
What is the complement of an event?
The complement Ac contains all outcomes where A does not occur. Their probabilities add to 1, so P(Ac) = 1 − P(A). Complement reasoning is especially useful for “at least one” questions.
How do I convert probability to odds in favor?
If probability is p, odds in favor can be written p:(1−p) and then scaled to a convenient ratio. For p = 0.25, the ratio is 0.25:0.75 = 1:3.
When are two events independent?
Events A and B are independent when knowing that one occurred does not change the probability of the other. Algebraically, P(A and B) = P(A)P(B), assuming the probabilities are defined.
Can probability be negative or greater than 1?
No. A valid probability lies between 0 and 1 inclusive. Percent form lies between 0% and 100%. Values outside that interval signal an invalid model, incompatible inputs, or an arithmetic error.
Formula Explorer connections
Interpretation: This formula summarizes data, models uncertainty or supports inference about a population or random process. Assumption: The sampling design and distribution assumptions must match the data. Independence, sample size, outliers and measurement quality can materially affect interpretation.