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?

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 2 years ago

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

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