If the probability of a student taking a calculus class is 0.10, the probability of taking a statistics class is 0.90, and the probability o

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If the probability of a student taking a calculus class is 0.10, the probability of taking a statistics class is 0.90, and the probability of taking a calculus class and a statistics class is 0.07, what is the probability of a student taking a calculus class or a statistics class

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Brielle 2 months 2021-10-21T00:41:28+00:00 1 Answer 0 views 0

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    2021-10-21T00:43:25+00:00

    Answer:

    93% probability of a student taking a calculus class or a statistics class

    Step-by-step explanation:

    We solve this problem building the Venn’s diagram of these probabilities.

    I am going to say that:

    A is the probability that a student takes a calculus class.

    B is the probability that a student takes a statistics class.

    We have that:

    A = a + (A \cap B)

    In which a is the probability that a student takes calculus but not statistics and A \cap B is the probability that a student takes both these classes.

    By the same logic, we have that:

    B = b + (A \cap B)

    The probability of taking a calculus class and a statistics class is 0.07

    This means that A \cap B = 0.07

    The probability of taking a statistics class is 0.90

    This means that B = 0.9. So

    B = b + (A \cap B)

    0.9 = b + 0.07

    b = 0.83

    The probability of a student taking a calculus class is 0.10

    This means that A = 0.1

    A = a + (A \cap B)

    0.1 = a + 0.07

    a = 0.03

    What is the probability of a student taking a calculus class or a statistics class

    A \cup B = a + b + A \cap B = 0.03 + 0.83 + 0.07 = 0.93

    93% probability of a student taking a calculus class or a statistics class

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