ACC 333 (Farrell)
Classes 26 & 27
Fall 2011
Page 1 of 7
Additional Study Questions
Probability and Decision Trees
1. Parts Problems
A manufacturing firm receives shipments of parts from two different suppliers, Ace Company and Action
Company.
Currently, 65% of the parts purchased by the company are from Ace, and the remaining are from
Action.
The quality of the purchased parts varies with the source of supply.
Based on historical data, the conditional
probabilities of receiving good and bad parts are:
Good Parts
Bad Parts
Ace Company
.98
.02
Action Company
.95
.05
If a part is found to be bad, what is the probability that it came from Ace?
From Action?
2.
Prospect Fields in Oil and Gas
An oil company’s geological assessment indicates that there’s a 25% chance that a particular prospect field
will produce oil.
Further, there’s an 80% chance that a particular well will strike oil given that oil is present
in the field.
Suppose that one well is drilled on the field and it comes up dry.
What is the probability that the
prospect field will produce oil?
3. Predicting the Weather
Suppose that you believe the chance that it will rain is 30%.
When you are watching television, the weather
person tells you that it’s going to rain tomorrow.
Suppose that you know that the weather person is pretty
good, and makes mistakes only 10% of the time.
In other words, if it’s actually going to rain tomorrow the
weather person says it’s going to rain with probability 0.9 and says it’s not going to rain with probability 0.1;
if it’s not going to rain tomorrow she says it’s going to rain with probability 0.1 and says it’s not going to rain
with probability 0.9.
Using Bayes’ Theorem, calculate what the probability of rain tomorrow is after hearing the weather person’s
prediction that it will rain.
4. Screening for Disease
Suppose there is a screening test for a rare disease, and that one person in 10,000 actually has the disease.
The screening test used to show if a person has the disease is quite good  if a person has the disease the test
will come back positive with certainty, and if a person does not have the disease the test will give a negative
result 99 times out of 100, but will one time out of 100 (that is, with probability 0.01) give a positive result (a
“false positive”).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 Anne
 Conditional Probability, Probability, Bayesian probability

Click to edit the document details