Assignment:
Q1. Mini Car Motors offers its luxury car in three colors: gold, silver and blue. The vice president of advertising is interested in the order of popularity of the color choices by customers during the first month of sales.
a. How many sample points are there in this experiment?
b. If the event A = gold is the most popular color, list the outcome(s) in event A.
c. If the event B = blue is the least popular color, list the outcome(s) in AB.
d. List the outcome(s) in ABc.
Sample Space
Q2. 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?
Basic relationships of probability
Q3. 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?
Bayes' theorem
Q4. 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?
Provide complete and step by step solution for the question and show calculations and use formulas.