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1 June, 05:59

Iven that, in a certain school, the following are true, what is the probability that a student is taking both math and computer science?

1. The probability that a student is taking math is 23%.

2. The probability that a student is taking computer science is 45%.

3. The probability that a student is taking math or computer science is 58%.

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Answers (1)
  1. 1 June, 08:20
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    The probability that a student is taking both math and computer science

    P (M∩CS) = 0.10

    Step-by-step explanation:

    Explanation:-

    Given data the probability that a student is taking math is 23%

    Let 'M' be the event of a student is taking math

    P (M) = 0.23

    Let 'CS' be the event of a student is taking computer science

    Given data the probability that a student is taking computer science is 45%

    P (CS) = 0.45

    Given the probability that a student is taking math or computer science is 58%.

    P (M U CS) = 0.58

    Addition theorem on probability

    If S is a sample size, and E₁ and E₂ be the events in S then

    P (E₁ or E₂) = P (E₁) + P (E₂) - P (E₁ and E₂)

    or

    P (E₁ ∪E₂) = P (E₁) + P (E₂) - P (E₁ ∩ E₂)

    Now

    P (M∪ CS) = P (M) + P (CS) - P (M∩CS)

    0.58 = 0.23 + 0.45 - P (M∩CS)

    P (M∩CS) = 0.68 - 0.58

    P (M∩CS) = 0.10

    Conclusion:-

    The probability that a student is taking both math and computer science

    P (M∩CS) = 0.10
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