31. Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40
a. What is P(A B)?
b. What is P(A | B)?
c. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusively they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
d. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
35. The US Bureau of Labor Statistics collected data on the occupations of workers 25 to
64 years old. The following table shows the number of male and female workers (in thousands) in each occupation category (Statistical Abstract of the United States:2002)
Occupation Male Female
Managerial/professional 19079 19021
Tech./Sales/Administrative 11079 19315
Service 4977 7947
Precision Production 11682 1138
Operators/Fabricators/Labor 10576 3482
Farming/Forestry/Fishing 1838 514
A. Develop a joint probability table.
B. What is the probability of a female worker being a manager or professional?
C. What is the probability of a male worker being in precision production?
D. Is occupation independent of gender? Justify your answer with a probability
37. A purchasing agent placed rush orders for a particular raw material with two different suppliers, A and B. If neither order arrives in four days, the production process must be shut down until at least one of the order arrives. The probability that supplier B can deliver the material in four days is .35
A. what is the probability that both suppliers will deliver the material in four days?
Because two separate suppliers are involved, we are willing to assume independence.
B. What is the probability that at least one supplier will deliver the material in four days.
C. What is the probability that the production process will be shut down in four days because of a shortage of raw material (i.e., both orders are lately)?
Calculations of independence of events, probability, joint probability and conditional probability.
Three questions on probability
1) Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour. For a patient selected at random:
a) What is the probability that the drug will be effective for 2 hours or less?
b) 1 hour or less?
c) 3 hours or more?
2) Life span for red foxes follow an approximately normal distribution with mean 7 years and standard deviation 3.5 years.
a) Find the probability that a red fox chosen at random will live at least 10 years.
b) Find the probability that a random sample of 4 red foxes will have a sample mean life span of over 10 years.
3) Margot has found that the mean time to run a job at the college copy center is 12.6 minutes with standard deviation 10 minutes. She selects a random sample of 64 jobs.
a) What is the probability that the sample mean copying time is between 14 and 15 minutes?
b) What is the probability that the sample mean copying time for this sample is between 10 and 12 minutes?