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  shock resistance

high low

scratch

resistance

high

low

70 9

16 5

Question 1 

KQ 2024 (Cooperative Learning 1)

 

In an acid-base titration, a base or acid is gradually added to the other until they have completelyneutralized each other. Because acids and bases are usually colorless (as are the water and salt

 produced in the neutralization reaction), pH is measured to monitor the reaction. Suppose that theequivalence point is reached after approximately 100 mL of a NaOH solution have been added

(enough to react with all the acetic acid present) but that replicates are equally likely to indicate

from 95 to 104 mL to the nearest mL. Assume that volumes are measured to the nearest mL anddescribe the sample space.

(a) What is the probability that equivalence is indicated at 100 mL?

(b) What is the probability that equivalence is indicated at less than 100 mL?

(c) What is the probability that equivalence is indicated between 98 and 102 mL (inclusive)?

Question 2 

Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance.The results from 100 disks are summarized as follows:

Let A denote the event that a disk has high shock resistance, and let B denote the event that adisk has high scratch resistance. If a disk is selected at random, determine the following

 probabilities: 

(a)  P ( A) (c)  P ( A′) (e)

(b)  P ( B) (d)  P ( A ∩  B) (f) 

 P ( A  B) 

 P (  A'  B)

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Question 3 

 Number of pages viewed: 1 2 3

4 ormore

Percentage of visitors: 40 30 20 10 

Percentage of visitors in each page-view category that provide

contact information: 10 10 20 40 

An article in the  British Medical Journal [“Com parison of Treatment of Renal Calculi byOperative Surgery, Percutaneous Nephrolithotomy, and Extracorporeal Shock Wave

Lithotripsy” (1986, Vol. 82, pp. 879 – 892)] provided the following discussion of success rates

in kidney stone removals. Open surgery had a success rate of 78% (273/350) while a newer

method, percutaneous nephrolithotomy (PN), had a success rate of 83% (289/350). This newermethod looked better, but the results changed when stone diameter was considered. For stones

with diameters less than two centimeters, 93% (81/87) of cases of open surgery were successful

compared with only 83% (234/270) of cases of PN. For stones greater than or equal to twocentimeters, the success rates were 73% (192/263) and 69% (55/80) for open surgery and PN,

respectively. Open surgery is better for both stone sizes, but less successful in total. In 1951,

E. H. Simpson pointed out this apparent contradiction (known as Simpson's Paradox) but the

hazard still persists today. Explain how open surgery can be better for both stone sizes butworse in total.

Question 4 

A company that tracks the use of its web site determined that the more pages a visitor views,

the more likely the visitor is to provide contact information. Use the following tables to answer

the questions:

(a) What is the probability that a visitor to the Web site provides contact information?

(b) If a visitor provides contact information, what is the probability that the visitorviewed four or more pages?

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Question 5 

Gene 1 Dominant Regressive Other

Dominant 5  25  30

Regressive 7  63  35

Other 20  15  800

 Natural red hair consists of two genes. People with red hair have two dominant genes, tworegressive genes, or one dominant and one regressive gene. A group of 1000 people was

categorized as follows:

Gene 2 

Let A denote the event that a person has a dominant red hair gene and let  B denote the eventthat a person has a regressive red hair gene. If a person is selected at random from this group,compute the following.

(a)  P ( A) (d) P ( A′ ∩  B)

(b)  P ( A ∩  B) (e) P ( A| B)

(c)  P ( A  B)  (f) Probability that the selected person has red hair