Problems in Math for decision making

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?

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