Probability Calculator

Coin Toss Probability

Calculate the probability of getting a specific number of heads in a series of coin tosses.

Number of Tosses:

Number of Heads:

Probability: 0.246

Dice Roll Probability

Calculate the probability of rolling a specific sum with multiple dice.

Number of Dice:

Desired Sum:

Probability: 0.167

Card Draw Probability

Calculate the probability of drawing specific cards from a standard deck.

Number of Cards Drawn:

Card Type:

Successful Draws:

Probability: 0.344

Binomial Distribution

Calculate probability with fixed number of trials with success/failure outcomes.

Number of Trials (n):

Probability of Success (p):

Number of Successes (k):

Probability P(X = k): 0.246

Cumulative P(X ≤ k): 0.623

Normal Distribution

Calculate probabilities for normally distributed random variables.

Mean (μ):

Standard Deviation (σ):

Calculate:

Value (x):

Upper Bound (b):

Probability: 0.5

Poisson Distribution

Calculate probability for events occurring in a fixed interval.

Average Rate (λ):

Number of Events (k):

Probability P(X = k): 0.224

Cumulative P(X ≤ k): 0.423

Bayes' Theorem

Calculate conditional probability using Bayes' theorem.

Prior Probability P(A):

Likelihood P(B|A):

False Positive Rate P(B|not A):

Posterior Probability P(A|B): 0.75

Bayesian Updating

Update probability estimates based on new evidence.

Prior Probability:

Number of Evidence Items:

Evidence 1 Likelihood Ratio:

Evidence 2 Likelihood Ratio:

Evidence 3 Likelihood Ratio:

Updated Probability: 0.55

Confidence Interval

Calculate confidence intervals for sample means.

Sample Mean:

Sample Standard Deviation:

Sample Size:

Confidence Level:

Confidence Interval: 46.4 to 53.6

Margin of Error: ±3.6

Monte Carlo Simulation

Estimate probabilities using Monte Carlo simulation.

Simulation Type:

Parameter 1:

Parameter 2:

Number of Trials:

Estimated Probability: 0.324

95% Confidence Range: ±0.029

Hypothesis Testing

Perform statistical hypothesis tests for means.

Test Type:

Sample Mean:

Sample Standard Deviation:

Sample Size:

Null Hypothesis Value:

Alternative Hypothesis:

Test Statistic: 1.10

p-value: 0.280

Result: Fail to reject null hypothesis

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Probability Calculators