Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that

Question

Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 65% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 10% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis. (Round your response to 4 decimal places).

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Amity 5 years 2021-09-04T15:08:51+00:00 1 Answers 23 views 0

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  1. King
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    2021-09-04T15:10:26+00:00
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    Answer:

    0.8125 = 81.25% probability that she or he used the lab on a regular basis.

    Step-by-step explanation:

    Conditional Probability

    We use the conditional probability formula to solve this question. It is

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

    In which

    P(B|A) is the probability of event B happening, given that A happened.

    P(A \cap B) is the probability of both A and B happening.

    P(A) is the probability of A happening.

    In this question:

    Event A: Student got an A

    Event B: Went to the lab on a regular basis

    Probability of a student getting an A:

    65% of 40%(go to the lab on a regular basis).

    10% of 100 – 40 = 60%(don’t go to the lab on a regular basis).

    So

    P(A) = 0.65*0.4 + 0.1*0.6 = 0.32

    Probability of getting an A and going to the lab on a regular basis:

    65% of 40%. So

    P(A \cap B) = 0.65*0.4 = 0.26

    Determine the probability that she or he used the lab on a regular basis.

    P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.26}{0.32} = 0.8125

    0.8125 = 81.25% probability that she or he used the lab on a regular basis.

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