Question

Answer the following questions and use Excel to show your work.

50 students in two sections of a college Physics 101 course recently took a mid-term exam. 13 students earned an A, 10 students earned a B, 8 students earned a C, 9 students earned a D, and 10 students earned an F on the exam. The students were queried regarding the number of hours they had devoted to studying for the exam. 12 of the students who earned an A, 8 of the students who earned a B, 6 of the students who earned a C, 2 of the students who earned a D, and 1 of the students who earned an F reported that they had devoted more than 8 hours to studying for the exam. The remaining students reported that they had devoted no more than 8 hours to studying for the exam.

1. What is the probability of a randomly-selected student having earned an A on the exam?

1. 0.15
2. 0.26
3. 0.32
4. 0.07

2. What is the probability of a randomly-selected student having earned an F on the exam?

1. 0.20
2. 0.27
3. 0.36
4. 0.17

3. What is the probability of a randomly-selected student having devoted no more than 8 hours to studying for the exam?

1. 0.51
2. 0.34
3. 0.42
4. 0.29

4. What is the probability of a randomly-selected student having earned an A on the exam given they devoted no more than 8 hours to studying for the exam?

1. 0.12
2. 0.21
3. 0.17
4. 0.05

5. What is the probability of a randomly-selected student having earned an F on the exam given they devoted more than 8 hours to studying for the exam?

1. 0.12
2. 0.03
3. 0.09
4. 0.17

6. What is the probability of a randomly-selected student having earned an A or a B on the exam given they devoted more than 8 hours to studying for the exam?

1. 0.57
2. 0.47
3. 0.69
4. 0.76

Answer 1

The table is as follows

	A	B	C	D	F	Total
> 8 hours	12	8	6	2	1	29
8 hours	1	2	2	7	9	21
Total	13	10	8	9	10	50

Probability = Favorable Outcomes / Total Outcomes

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(1) P(getting an A) = 13 / 50 = 0.26 (Option b)

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(2) P(getting an F) = 10 / 50 = 0.20 (Option A)

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(3) P(No More than 8 hours) = 21 / 50 = 0.42 (Option c)

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(4) P(Getting an A given that they did not spend more than 8 Hours)

By Bayes Theorem: P(A given B) = P(A and B) / P(B) = (1/50) / (21/50) = 1/21 = 0.05 (Option d)

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(5) P(Getting an F given that they spent more than 8 Hours)

By Bayes Theorem: P(A given B) = P(A and B) / P(B) = (1/50) / (29/50) = 1/29 = 0.03 (Option b)

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(6) P(Getting an A or B given that they spent more than 8 Hours)

By Bayes Theorem: P(A given B) = P(A and B) / P(B) = [(12 + 8)/50] / (29/50) = 20/29 = 0.69 (Option c)

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