Probability Calculator

    Calculate probabilities, odds, and statistical distributions

    Probability Calculator

    About Probability

    Probability measures the likelihood that an event will occur. It ranges from 0 (impossible) to 1 (certain), and can be expressed as a decimal, fraction, or percentage.

    •Basic Probability

    P(A) = Number of favorable outcomes / Total number of outcomes

    •Binomial Probability

    P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

    –n = number of trials
    –k = number of successes
    –p = probability of success on each trial
    –C(n,k) = combinations of n things taken k at a time

    •Key Concepts

    –
    Complement:P(not A) = 1 - P(A)
    –
    Odds:Ratio of favorable to unfavorable outcomes
    –
    Independent Events:One event doesn't affect another
    –
    Mutually Exclusive:Events cannot occur simultaneously

    •Applications

    • –Games of chance and gambling
    • –Quality control and testing
    • –Medical diagnosis and treatment
    • –Weather forecasting
    • –Insurance and risk assessment
    • –Scientific research

    •Examples

    –
    Coin flip:P(heads) = 1/2 = 0.5 = 50%
    –
    Die roll:P(rolling 6) = 1/6 ≈ 0.167 = 16.7%
    –
    Card draw:P(ace from deck) = 4/52 ≈ 0.077 = 7.7%

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