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18 November, 09:57

Zoe has a chance of receiving an A grade in statistics, a chance of receiving an A grade in mathematics, and a chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).

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  1. 18 November, 11:24
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    Question:

    Zoe has a 67% chance of receiving an A grade in statistics, a 51% chance of receiving an A grade in mathematics, and a 41% chance of receiving A grades in both statistics and mathematics. Find the probability that she receives an A in statistics or mathematics (or both).

    Answer:

    The answer to the question is;

    The probability that she receives an A in statistics or mathematics (or both) is 77%. which is a probability of 0.77.

    Step-by-step explanation:

    To solve the question we have

    P (S) = Chance of having A grade in statistics = 67 %

    P (A) = Chance of having A grade in mathematics = 51 %

    P (S) ∩P (A) = Chance of having A grade in both mathematics and statistics

    = 41 %

    Therefore the chance of having an A grade in only statistics is given by

    P (S) - P (S) ∩P (A) = 67 - 41 = 26 % similarly

    The chance of having an A grade in only mathematics is given by

    P (A) - P (S) ∩P (A) = 51 - 41 = 10 %

    Therefore the chance of having an A grade in statistics or mathematics (or both) is given by

    P (S) - P (S) ∩P (A) + P (A) - P (S) ∩P (A) + P (S) ∩P (A)

    = 26 + 10 + 41 = 77%
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