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    IBHardProbability10–12

    Bayes' Theorem

    Teorema de Bayes

    A disease affects 1\% of a population. A test is 95\% accurate (for both positives and negatives). If someone tests positive, what is the actual probability they have the disease?

    Use Bayes' theorem: P(D|+) = \frac{P(+|D) \cdot P(D)}{P(+)}. Calculate P(+) using the law of total probability.

    Solution

    Step 1 of 4

    1. 1.P(D) = 0.01, P(+|D) = 0.95, P(+|\neg D) = 0.05