Download Conditional Probability Name: Alg2 CC Conditional Probability A

Conditional Probability
Alg2 CC
Name:
Conditional Probability
A researcher is interested in evaluating how well a diagnostic test works
for detecting renal disease in patients with high blood pressure. She
performs a diagnostic test on 137 patients – 67 with known renal disease
and 70 who are known to be healthy. The diagnostic test comes back either
positive (the patient has renal disease) or negative (the patient does not
have renal disease). Here are the results of her experiment.
Let the following letters stand for the following events,
R = known Renal Disease
H = known Healthy
P = tested Positive
N = tested Negative
If a patient is picked at random, find the probability that the patient:
a) tested negative 𝑃(𝑁)
b) was known to have Renal Disease 𝑃(𝑅)
c) tested negative given they were known to have Renal Disease 𝑃(𝑁|𝑅).
d) Which is more likely, that a patient picked at random will test positive, given they were healthy
𝑃(𝑃|𝐻), or that a patient test positive given they have Renal Disease 𝑃(𝑃|𝑅)? Show the calculations
for both.
Conditional Probability Practice
Alg2 CC
Name:
1) In the Venn diagram shown below, the total sample space is 60. Each dot represents an equally likely
outcome of the sample space. Some of these fall only into event A, some only into event B, some in both
events and some in neither.
𝑛(𝐵) = __________
𝑛(𝐴 𝑎𝑛𝑑 𝐵) = _____________
𝑛(𝑆) = __________
Consider the probability of A occurring given that B has occurred,
Show that the formula for this probability is based on counting the
number of elements in each set and their intersection.
𝑃(𝐴|𝐵) =
P( Aand B)
n( Aand B)
=
P( B)
n( B )
2) Using the Venn diagram of Lewis HS,
a. find 𝑃(𝐴|𝐵)
b. find 𝑃(𝐵|𝐴)
3)
Find the probability that a randomly selected dog is
a. A Basset Hound, given it is female
b. Male, given it is a Boxer.
4)
5)
6)
More practice!
7)
8) Andrea is a very good student. The probability that she studies and passes her mathematics test is
17/20. If the probability that Andrea studies is 15/16, find the probability that Andrea passes her
mathematics test, given that she has studied.
9) The probability that Sue will go to Mexico in the winter and to France in the summer is 0.40. The
probability that she will go to Mexico in the winter is 0.60. Find the probability that she will go to
France this summer, given that she just returned from her winter vacation in Mexico.
10) High school students in one school chose their favorite leisure activity. Find each probability. Round to the
nearest tenth of a percent.