(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


please help me with number 7IEOR E3658

 

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%

 

college graduate

 

(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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