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    IBMediumProbability7–9

    Two Sports, One Class: Overlap and Probability

    Dois Desportos, Uma Turma: Sobreposição e Probabilidade

    In a class of 3030 students, 1818 play football, 1414 play volleyball and 55 play neither sport. One student is chosen at random. Find the probability that the student plays both sports, and the probability that the student plays exactly one of them.

    The two counts overlap, so adding them counts some students twice. Work out how many students play at least one sport before you touch the overlap, and remember that "exactly one" excludes the overlap rather than including it.

    Solution

    Step 1 of 11

    1. 1.Students playing at least one sport: