please help me with number 7IEOR E3658
Homework 2 - Conditional Probability
Due on September 23rd, in class
1. In the 2004 presidential election, exit polls from the critical state of Ohio provided the
no college degree
If a randomly selected respondent voted for Bush, what is the probability that the
person has a college degree?
2. A new analytical method to detect pollutants in water is being tested. This new method
of chemical analysis is important because, if adopted, it could be used to detect three
di erent contaminants - organic pollutant, volatile solvents, and chlorinated compounds
- instead of having to use a single test for each pollutant. The makers of the test claim
that it can detect high levels of organic pollutant with
accuracy, volatile solvents
accuracy, and chlorinated compounds with
accuracy. If a pollutant
is not present, the test does not signal. Samples are prepared for the calibration of
the test and
of them are contaminated with organic pollutants,
with traces of chlorinated compounds. A test sample is selected
(a) What is the probability that the test will signal?
(b) If the test signals, what is the probability that chlorinated compounds are present?
The following circuit operates if and
onlyif there is a path of functional
devices from left to right.
that devices fail independently and
the probability of
of each de-
vice is as shown. What is the proba-
bility that the circuit does not oper-
4. Eight rooks are placed in distinct squares of an
chessboard, with all possible
placements being equally likely. Find the probability that all the rooks are safe from
one another, i.e., that there is no row or column with more than one rook.
This question was answered on: May 23, 2022
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