A professor has noticed that students hat attend class regularly, mss no more th

Question

A professor has noticed that students hat attend class regularly, mss no more than two classes per term, generally get better grades. For he class, the overall percent o students who attend regularly s 72% or those who come to class on a regular basis, 51% receive A's. Of those who don't attend regularly, only 10% get A's. Draw a tree diagram like the one in the image, where R-"attends class regularly", R'-"does not attend class regularly. A-"earned an A. A'-"did not earn an A" (a) Based on your tree diagram fill in the appropriate matching probabilities, enter your answer as a proportion with three decimal places.: A. or P(R)51 B. or P(R')1 C. or P(AIR) D. or PAR) E. or P(AIR') T. or P(A'IR)- (b)Among all students what proportion earn an A and don't attend class regularly? (c)What is the chance a randomly chosen student will earn an A in the class? (d)Given a student eamed an A, what is the chance they attend class regularly? Hint: Use the total aw of probability Hint: P(RIA)

Explanation / Answer

A)
a)0.72
b)1-0.72=0.28
c)
0.51
d)
1-0.51=0.49
e)
0.10
f)
1-0.10=0.9

B)
P(earn A and don't attend class regularly)
= P(A and R')
= P(A|R') P(R')
= 0.28*0.10
=0.028
c)
P(A) = P(A|R') P(R') + P(A|R) P(R)
= 0.028 + 0.72 * 0.51
= 0.3952
d)
P(R|A) = P(R and A) /P(A)
= 0.72*0.51 / 0.3952
= 0.9291497

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