10 points In a particular college statistics course, twenty percent of the stude

Question

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. 7 (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

a) P(taken statistics and receive and A)= 0.2*0.25=0.05

b)P(received A) =P(taken statistics and receive and A)+P(not taken statistics and receive and A)

=0.2*0.25+(1-0.2)*0.15=0.17

c) therefore probability of not taken statisitc course given received A

=P(not taken statistics and receive and A)/P(received A) =(1-0.2)*0.15/0.17 =0.7059

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