In a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students p

Question

In a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams. Assume a randomly selected student is selected from the class. If the student passed the first exam, what is the probability that they passed the second exam?

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Adalyn 2 weeks 2021-09-11T17:05:52+00:00 1 Answer 0

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    2021-09-11T17:06:53+00:00

    Answer:

    Required probability is 0.784 .

    Step-by-step explanation:

    We are given that in a large statistics course, 74% of the students passed the first exam, 72% of the students pass the second exam, and 58% of the students passed both exams.

    Let Probability that the students passed the first exam = P(F) = 0.74

         Probability that the students passed the second exam = P(S) = 0.72

         Probability that the students passed both exams = P(F \bigcap S) = 0.58

    Now, if the student passed the first exam, probability that he passed the second exam is given by the conditional probability of P(S/F) ;

    As we know that conditional probability, P(A/B) = \frac{P(A\bigcap B)}{P(B) }

    Similarly, P(S/F) = \frac{P(S\bigcap F)}{P(F) } = \frac{P(F\bigcap S)}{P(F) }  {As P(F \bigcap S) is same as P(S \bigcap F) }

                              = \frac{0.58}{0.74} = 0.784

    Therefore, probability that he passed the second exam is 0.784 .

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45:7+7-4:2-5:5*4+35:2 =? ( )