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Chapter 3: Q95SE (page 203)

A sample space consists of three sample points,S1,S2,S3, withP(S1)=0.1, andP(S2)=0.2.

  1. Assign a probability toS3in a way that the three sample points define a valid sample space obeying the two probability rules.
  2. If an eventA={S2,S3}, find P(A).

Short Answer

Expert verified

Therefore, the results are

  1. PS3=0.7
  2. PA=0.5

Step by step solution

01

Given information 

Here A sample space consists of three sample points,S1,S2,S3 , with P(S1)=0.1, andP(S2)=0.2 .

02

Define a valid space

a.

According to the question

Assign a probability toS3 in a way that the three sample points.

P(S1)=0.1, and P(S2)=0.2so,

P(S3)=0.7

P(S1)+P(S2)+P(S3) = 10.1+0.2+PS3=1PS3=1-0.3PS3=0.7

Hence, PS3=0.7

03

Find P(A).

b.

If an eventA={S2,S3} , then,

P(A)=P(S2)+P(S3)=0.2+0.3=0.5

Therefore,PA=0.5

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Most popular questions from this chapter

Speeding linked to fatal car crashes. According to the National Highway Traffic and Safety Administration’s National Center for Statistics and Analysis (NCSA), “Speeding is one of the most prevalent factors contributing to fatal traffic crashes” (NHTSA Technical Report, August 2005). The probability that speeding is a cause of a fatal crash is .3. Furthermore, the probability that speeding and missing a curve are causes of a fatal crash is .12. Given speeding is a cause of a fatal crash, what is the probability that the crash occurred on a curve?

Exit poll candidates and voters.In an exit poll, 45% of voters said that the main issue affecting their choice of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choice of candidates.

  1. List the sample points for this experiment.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the main issue affecting randomly selected voters’ choice was either the economy or national security?

Reliability of gas station air gauges. Tire and automobile manufacturers and consumer safety experts all recommend that drivers maintain proper tire pressure in their cars. Consequently, many gas stations now provide air pumps and air gauges for their customers. In a Research Note(Nov. 2001), the National Highway Traffic Safety Administration studied the reliability of gas station air gauges. The next table gives the percentage of gas stations that provide air gauges that over-report the pressure level in the tire.

a. If the gas station air pressure gauge reads 35 psi, what is the probability that the pressure is over-reported by 6 psi or more?

b. If the gas station air pressure gauge reads 55 psi, what is the probability that the pressure is over-reported by 8 psi or more?

c. If the gas station air pressure gauge reads 25 psi, what is the probability that the pressure is not over-reported by 4 psi or more?

d. Are the events A= {over report by 4 psi or more} and B= {over report by 6 psi or more} mutually exclusive?

e.Based on your answer to part d, why do the probabilities in the table not sum to 1?

Social networking Web sites in the United Kingdom. In the United States, MySpace and Facebook are considered the two most popular social networking Websites. In the United Kingdom (UK), the competition for social networking is between MySpace and Bebo. According to Nielsen/ Net Ratings (April 2006), 4% of UK citizens visit MySpace, 3% visit Bebo, and 1% visit MySpace and Bebo.

a. Draw a Venn diagram to illustrate social networking sites in the United Kingdom.

b. Find the probability that a UK citizen visits either the MySpace or Bebo social networking site.

c. Use your answer to part b to find the probability that a UK citizen does not visit either social networking site.

Guilt in decision making.Refer to the Journal of Behavioral Decision Making(January 2007) study of theeffect of guilt emotion on how a decision maker focuseson a problem, Exercise 3.48 (p. 183). The results (numberresponding in each category) for the 171 study participantsare reproduced in the table below. Suppose one of the 171participants is selected at random.

Emotional

State

Choose

Stated Option

Do Not Choose

Stated Option

Totals

Guilt

Anger

Neutral

45

8

7

12

50

49

57

58

56

Totals

60

111

171

a.Given that the respondent is assigned to the guilty state, what is the probability that the respondent chooses the stated option?

b.If the respondent does not choose to repair the car, what is the probability that the respondent is in the anger state?

c.Are the events {repair the car} and {guilty state }
independent?
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