Last year at Townsburg High School, 30% of the graduating seniors took the ACT exam, 37% of the graduating seniors took the SAT exam, and 22

Question

Last year at Townsburg High School, 30% of the graduating seniors took the ACT exam, 37% of the graduating seniors took the SAT exam, and 22% of graduating seniors too both exams. A student is selected at random. If the student took the ACT, what is the probability that they also took the SAT?

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Piper 3 hours 2021-09-15T00:26:30+00:00 1 Answer 0

Answers ( )

  1. Answer:

    73.33% probability that they also took the SAT

    Step-by-step explanation:

    We have these following two events.

    Event A: Taking the ACT exam. So P(A) = 0.3.

    Event B: Taking the SAT exam. So P(B) = 0.37.

    The conditional probability formula is:

    P(B|A) = \frac{P(A \cap B)}{P(B)}

    In which P(B|A) is the probability of event B happening given that A has happened, P(A \cap B) is the probability of both events hapenning.

    22% of graduating seniors too both exams.

    This means that P(A \cap B) = 0.22

    If the student took the ACT, what is the probability that they also took the SAT?

    P(B|A) = \frac{P(A \cap B)}{P(B)} = \frac{0.22}{0.3} = 0.7333

    73.33% probability that they also took the SAT

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