(Solution) IEOR E3658 Homework 2 - Conditional Probability Fall 2013 Due On September 23rd, In Class 1. In The 2004 Presidential Election, Exit Polls From The | Snapessays.com

(Solution) IEOR E3658 Homework 2 - Conditional Probability Fall 2013 Due on September 23rd, in class 1. In the 2004 presidential election, exit polls from the

Homework 2 - Conditional Probability

Fall 2013

Due on September 23rd, in class

1. In the 2004 presidential election, exit polls from the critical state of Ohio provided the

following results:

Bush

Kerry

no college degree

(62%)

50%

50%

(38%)

53%

46%

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

99

.

7%

accuracy, volatile solvents

with

99

.

95%

accuracy, and chlorinated compounds with

89

.

7%

accuracy. If a pollutant

is not present, the test does not signal. Samples are prepared for the calibration of

the test and

60%

of them are contaminated with organic pollutants,

27%

with volatile

solvents, and

13%

with traces of chlorinated compounds. A test sample is selected

randomly.

(a) What is the probability that the test will signal?

(b) If the test signals, what is the probability that chlorinated compounds are present?

3.

The following circuit operates if and

onlyif there is a path of functional

devices from left to right.

Assume

that devices fail independently and

the probability of

failure

of each de-

vice is as shown. What is the proba-

bility that the circuit does not oper-

ate?

0.02

0.02

0.01

0.01

0.01

0.01

4. Eight rooks are placed in distinct squares of an

8

×

8

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.

1

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