Examples for

# Probability

Probability is the quantification of the likelihood that an event or a set of events will occur. Using Wolfram|Alpha's broad computational understanding of probability and expansive knowledge of real-world applications of probability theory, you can compute the chances of winning various games driven by random chance, conduct and analyze the experimental outcomes of random trials, visualize and compute the properties of probability distributions and calculate the probabilities of events given a set of conditions.

Compute winnings, analyze bets and determine outcomes for games of chance ranging from the toss of a coin to a game of poker and the draw of your local lottery numbers.

#### Compute coin-toss probabilities:

#### Compute dice probabilities:

#### Compute odds for a poker hand:

#### Analyze a bet in roulette:

#### Analyze a wager:

#### Get lottery odds:

### Birthday Probabilities

Compute the chance people in a group have of sharing a birthday or investigate the likelihood of people's birthdays falling in a specific date range or month or on a specific day of the week.

#### Compute the probability of shared birthdays in a group of people:

#### Specify the number of possible birthdays:

#### Compute the probability of shared birthdays for a given interval:

Determine the likelihood of any outcome for any number or specification of Bernoulli trials.

#### Compute probabilities for a sequence of trials:

#### Analyze waiting-time probabilities:

#### Find the probability of a run:

### Probability Formulas

Compute the probabilities of various compositions of events or specify individual probabilities to determine the likelihood of some, all or no events occurring.

#### Compute the probability of a union of events:

#### Compute a conditional probability:

#### Compute the probability of a complement:

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Statistics Web App### RELATED EXAMPLES

Compute a specific property of a probability distribution, the likelihood that an outcome has of occurring or explore the defining characteristics of a vast set of probability distributions.