Students in a statistics class were asked what grade they expected in the course

Question

Students in a statistics class were asked what grade they expected in the course and whether they worked additional problems beyond those assigned by the instructor. The table below gives the results Find the probability that a randomly chosen student from the class worked additional problems. What is the probability that a student expects an A? What is the probability that a student expects a B and worked extra problems? What is the probability that given a student worked the extra problems, he or she expects a C?

Explanation / Answer

A= student expected grade A

B= student expected grade B

C= student expected grade C

D= student expected grade below C

W= student worked on additional problems

WN= student not worked on additional problems

Lets take conditional probability,

P(W intersection A)=0.12

P(W intersection B)=0.06

P(W intersection C)=0.12

P(W intersection D)=0.02

a) probability that a randomly chosen student from the class worked additional problems

P(W)= P(W intersection A)+P(W intersection B)+P(W intersection C)+P(W intersection D)

        =0.12+0.06+0.12+0.02

P(W)=0.32

P(A)=0.25

P(W/A)= 0.12/0.25=0.48

P(W/A)=0.48

P(W/B)= P(W intersection B)/P(B)

           =0.06/0.27

P(W/B)=0.22

P(W/C)= P(W intersection C)/P(C)

           =0.12/0.38

P(W/C)=0.315

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