WHRHS
Algebra 3
Name ________________________________________________ Date ____________
Unit 10: Conditional Probability (Day 14)
A table can be used to organize information for complicated conditional probabilities.
Setup a table with a hypothetical population of 100,000 and calculate to probabilities.
1. We know that the prevalence of a particular disease is 1/1000 in the general
population. A test for this ailment has a false positive rate of 5%, that is, 5% of the
time the test will erroneously indicate that the disease is present when in fact it is
not. We are also told that 98% of the people with the disease will in fact test
positive. Assuming that you know nothing about particular individuals or their
symptoms, what is the probability that a person that has tested positive does in fact
have the disease?
2. A test for a genetic disorder can detect the disorder with 94% accuracy. However,
the test will incorrectly report positive results for 3% of those without the disorder.
If 12% of the population has the disorder, find the probability that a person testing
positive actually has the genetic disorder.
WHRHS
Algebra 3
3. A pharmaceutical company has developed a test for a scarce disease that is present
in 0.5% of the population. The test is 98% accurate in determining a positive result,
and the chance of a false positive is 4%. What is the probability that someone who
tests positive actually has the disease?
4. A company that performs drug testing guarantees that its test determines a positive
result with 97% accuracy. However, the test also gives 6% false positives. If 5% of
those being tested actually have the drug present in their bloodstream, find the
probability that a person testing positive has actually been using drugs.
WHRHS
Algebra 3
5. When used together, the ELISA and Western Blot tests for HIV are more than 99%
accurate in determining a positive result. The chance of a false positive is between
1 and 5 for every 100,000 tests. If we assume a 99% accuracy rate for correctly
identifying positive results and 5/100,000 false positives, find the probability that
someone who tests positive has HIV. (The Centers for Disease Control and
Prevention estimate that about 0.3% of U.S. residents are infected with HIV.)
6. A diagnostic test for eye disease is accurate 88% of the time and 2.4% of the
population actually has eye disease.
a. Determine the probability the patient tests positive.
b. Determine the probability the patient tests negative.
c. Determine the probability the patient has eye disease, given that they test
positive.
d. Determine the probability the patient does not have eye disease, given that
they test negative.
WHRHS
Algebra 3
7. The US agency for Healthcare Research and Quality indicates that about 30% of
women who undergo a biopsy actually have breast cancer. This type of biopsy has
a false-positive rate of 2% and a false-negative rate of 14%.
a. P(has cancer | positive test)
b. P(has cancer | negative test)
8. Your doctor tells you that you have tested positive for Statistics Deficit Disorder, a
very rare condition affecting 3 people in a 1,000 (0.3% of the population). She
assures you that the test is very accurate: 98% of affected people will get a positive
result, and it gives a false positive only 1% of the time.
a. Find P(have SDD | positive test)