Probability Review Problems
1.
The Texas Oil Company provides a limited partnership arrangement whereby small investors can pool
resources to invest in large-scale oil exploration program. In the exploratory drilling phase, the
selection of locations for new wells is based on the geologic structure of the proposed drilling sites.
Experience shows that the probability of a type A structure at the site of a productive well is 0.40. The
company also knows that 50% of all wells are drilled in locations with type A structure. Finally, 30%
of all wells drilled are productive.
a. What is the probability of a well being drilled in a type A structure and being productive?
b. If the drilling process begins in a location with a type A structure, what is the probability of having
a productive well at that location?
c. Is finding a productive well independent of the type A geologic structure? Explain.
2.
A company has studied the number of lost-time accidents occurring at its Brownsville, Texas plant.
Historical records show that 6% of the employees had lost-time accidents last year. Management
believes that a special safety program will reduce the accidents to 5% during the current year. In
addition, it estimates that 15% of those employees having had lost-time accidents last year will have a
lost-time accident during the current year.
a. What percentage of the employees will have lost-time accidents in both years?
b. What percentage of the employees will have at least one lost-time accident over the 2-year period?
3.
A purchasing agent has placed a rush order for a particular raw material with two different suppliers, A
and B. If neither order arrives in 4 days the production process must be shut down until at least one of
the orders arrives. The probability that supplier A can deliver the material in 4 days is 0.55. The
probability that supplier B can deliver the material in 4 days is 0.35.
a. What is the probability that both suppliers deliver the material in 4 days? Since two separate
suppliers are involved, assume independence.
b. What is the probability that at least one supplier delivers the material in 4 days?
c. What is the probability the production process is shut down in 4 days because of a shortage in raw
material (that is, both orders are late)?
4.
(hint: uses Bayes Theorem) A consulting firm has submitted a bid for a large research project. The
firm’s management initially felt there was 50-50 chance of getting the bid. However, the agency to
which the bid was submitted has subsequently requested additional information on the bid. Experience
indicates that on 75% of the successful bids and 40% of the unsuccessful bids the agency requested
additional information.
a. What is your prior probability the bid will be successful (i.e., prior to receiving the request for
additional information)?
b. What is the conditional probability of a request for additional information given that the bid will
ultimately be successful?
c. Compute a posterior probability that the bid will be successful given that a request for additional
information has been received.
5.
(hint: uses Bayes Theorem) A local bank is reviewing its credit card policy with a view toward
recalling some of its credit cards. In the past approximately 5% of cardholders have defaulted, and the
bank has been unable to collect the outstanding balance. Thus, management has established a prior
probability of 0.05 that any particular cardholder will default. The bank has further found that the
probability of missing one or more monthly payments for those customers who do not default is 0.20.
Of course, the probability of missing one or more payments for those who default is 1.
a. For a customer who has missed a monthly payment, compute the posterior probability that the
customer will default.
b. The bank would like to recall its card if the probability that customer will default is greater than
0.20. Should the bank recall its card if the customer misses a monthly payment? Why or why
not?