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    IBHardProbability10–12

    Binomial Probability

    Probabilidade Binomial

    A test has 10 multiple-choice questions, each with 4 options. If a student guesses randomly, what is the probability of getting exactly 5 correct? Use the binomial probability formula.

    Eleven separated vertical bars, one for each number of correct answers from 0 to 10, at their true relative heights. The bars rise to a peak at 2 correct, fall away steadily, and are almost invisible from 7 correct upward. The bar for 5 correct is shaded darker and labelled. The vertical axis is marked as the probability of k correct but carries no numeric scale.kP(X = k)012345678910k = 5

    Use P(X = k) = \binom{n}{k} \cdot p^{k} \cdot (1-p)^{n-k} where n=10 and k=5. Each question has four options and only one of them is right.

    Solution

    Step 1 of 5

    1. 1.P(X = 5) = \binom{10}{5} \cdot (0.25)^{5} \cdot (0.75)^{5}