7. [10 points] In a particular college statistics course, twenty percent of the

Question

7. [10 points] In a particular college statistics course, twenty percent of the students had previously taken a statistics course during high school while the others had not. Among those students who had taken a high school course, twenty-five percent received an A in their college course; while only fifteen percent of those students with no prior exposure received an A in the college course. Suppose that one student from the college course is selected at random. (a) Find the probability that they had taken statistics during high school and receive an A in their college course. [3 points] (b) Find the probability that they receive an A in the college course. [3 points] (c) Suppose that you overhear the student boasting about receiving an A in their college statistics course. Find the probability that they had not taken a statistics course during high school. [4 points]

Explanation / Answer

probability of previously taken statistic course in high school=P(S) =0.20

and not taken the course =P(Sc) =1-0.20=0.80

let probability of A =P(A)

therefore from above probability of A given taken the course =P(A|S) =0.25

probability of A given not taken the course =P(A|Sc) =0.15

a) probability of taken the course and received A =P(SnA) =P(S)*P(A|S) =0.20*0.25=0.05

b)probability of A =P(A)= P(S)*P(A|S)+P(Sc)*P(A|Sc) =0.2*0.25+0.8*0.15=0.17

c)probability of not taken the course given received an A =P(Sc|A) =P(Sc)*P(A|Sc) /P(A) =0.8*0.15/0.17=0.7059

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