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Probability Problems

1. There are two more assignments in a class before its end, and if you get an A on at least one of them, you will get an A for the semester. Your subjective assessment of your performance is:

Event Probability
A on paper and A on exam .25
A on paper only .10
A on exam only .30
A on neither .35

a. What is the probability of getting an A on the paper?
b. What is the probability of getting an A on the exam?
c. What is the probability of getting an A in the course?
d. Are the grades on the assignments independent?

2. A medical research project examined the relationship between a subject?s weight and recovery time from a surgical procedure, as shown in the table below.

Underweight Normal weight Overweight
Less than 3 days 6 15 3
3 to 7 days 30 95 20
Over 7 days 14 40 27

a. Use relative frequency to develop a joint probability table to show the marginal probabilities.
b. What is the probability a patient will recover in fewer than 3 days?
c. Given that recovery takes over 7 days, what is the probability the patient is overweight?

3. The Ambell Company uses batteries from two different manufacturers. Historically, 60% of the batteries are from manufacturer 1, and 90% of these batteries last for over 40 hours. Only 75% of the batteries from manufacturer 2 last for over 40 hours. A battery in a critical tool fails at 32 hours. What is the probability it was from manufacturer 2?

Solution Preview

Please see attached file.

Answer

Let E be the event that you get A for at least one assignment and F be the event that you get A for the examination.
Given that
P(Eï??F) = 0.25
P(Eï??F?) = 0.10
P(E?ï??F) = 0.30
P(E?ï??F?) = 0.35

a. What is the probability of getting an A on the paper?

P(E) = P(Eï??F) + P(Eï??F?)
=0.25+0.10
= 0.35

b. What is the probability of getting an A on the exam?

P(F) = P(Eï??F) + P(E?ï??F)
=0.25+0.30
=0.55

c. What is the probability of getting an A in the course?

P(Eï??F) = P(E)+P(F)- P(Eï??F)
= 0.35 + 0.55 -0.25
= 0.65

Alternative
P(Eï??F) = 1- P(E?ï??F?)
= 1- 0.35
= ...

Solution Summary

The solution gives the complete details of calculating probabilities of different events. Step by step solution is given with interpretations of the results.

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