Question

In: Statistics and Probability

Make an A Make a B Make a C Make a D Make an F Sophomores...

Make an A

Make a B

Make a C

Make a D

Make an F

Sophomores

.058

.101

.142

.092

.047

Juniors

.055

.082

.102

.071

.030

Seniors

.014

.023

.080

.063

.040

(a) What is the probability that a randomly selected student in Dr. Alan  Math course is a Sophomore?

(b) What is the probability that a randomly selected student will make a D in Dr. Alan  Math course?

(c) Given that a particular student made a B or better in Dr. Alan  Math course, what is the probability that he or she took the course as a Junior?

(d) Given that a particular student in Dr. Alan Math  course is a Senior, what is the probability that he or she will make an A in the course?

Solutions

Expert Solution

Make an A Make an B Make an C Make an D Make an F Total
Sophomores 0.058 0.101 0.142 0.092 0.047 0.44
Juniors 0.055 0.082 0.102 0.071 0.030 0.34
Seniors 0.014 0.023 0.080 0.063 0.040 0.22
Total 0.127 0.206 0.324 0.226 0.117 1

(a) What is the probability that a randomly selected student in Dr. Alan  Math course is a Sophomore?

P[ Sophomore ] = 0.44

Make an A Make an B Make an C Make an D Make an F Total
Sophomores 0.058 0.101 0.142 0.092 0.047 0.44
Juniors 0.055 0.082 0.102 0.071 0.030 0.34
Seniors 0.014 0.023 0.080 0.063 0.040 0.22
Total 0.127 0.206 0.324 0.226 0.117 1

(b) What is the probability that a randomly selected student will make a D in Dr. Alan  Math course?

Make an A Make an B Make an C Make an D Make an F Total
Sophomores 0.058 0.101 0.142 0.092 0.047 0.44
Juniors 0.055 0.082 0.102 0.071 0.030 0.34
Seniors 0.014 0.023 0.080 0.063 0.040 0.22
Total 0.127 0.206 0.324 0.226 0.117 1

P[ make an D ] = 0.226

(c) Given that a particular student made a B or better in Dr. Alan  Math course, what is the probability that he or she took the course as a Junior?

Make an A Make an B Make an C Make an D Make an F Total
Sophomores 0.058 0.101 0.142 0.092 0.047 0.44
Juniors 0.055 0.082 0.102 0.071 0.030 0.34
Seniors 0.014 0.023 0.080 0.063 0.040 0.22
Total 0.127 0.206 0.324 0.226 0.117 1

P[ Junior | made a B or better ] = ( 0.055 + 0.082 ) / ( 0.127 + 0.206 )

P[ Junior | made a B or better ] = 0.137/0.333

P[ Junior | made a B or better ] = 0.4114

(d) Given that a particular student in Dr. Alan Math  course is a Senior, what is the probability that he or she will make an A in the course?

Make an A Make an B Make an C Make an D Make an F Total
Sophomores 0.058 0.101 0.142 0.092 0.047 0.44
Juniors 0.055 0.082 0.102 0.071 0.030 0.34
Seniors 0.014 0.023 0.080 0.063 0.040 0.22
Total 0.127 0.206 0.324 0.226 0.117 1

P[ make an A | Senior ] = 0.014/0.22

P[ make an A | Senior ] = 0.0636

orchestra answered 3 years ago
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