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Chapter 3: Q64E (page 194)

Do social robots walk or roll?Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercises 3.10 (p. 168) and 3.37 (p. 181). Recall that in a random sample of 106 social robots, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. If a social robot is designed with wheels, what is the probability that the robot also has legs?

Short Answer

Expert verified

7.5%

Step by step solution

01

 Step 1: Random Sample

Random samplingis a sampling strategy in which every test has an equal chance of being selected. A random sample is intended to provide an impartial reflection of the overall population.

02

Finding the probability that the robot has wheels and legs

A = Robots with both legs and wheels (8)

B = Total number of robots (106)

P=RobotswithlegsandwheelsTotalRobots=8106=0.075=7.5%

Therefore, the probability that a robot designed with wheels also has legs is 7.5%.

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Most popular questions from this chapter

Inactive oil and gas structures. U.S. federal regulations require that operating companies clear all inactive offshore oil and gas structures within 1 year after production ceases. Researchers at the Louisiana State University Center for Energy Studies gathered data on both active and inactive oil and gas structures in the Gulf of Mexico (Oil & Gas Journal, Jan. 3, 2005). They discovered that the Gulf of Mexico has 2,175 active and 1,225 idle (inactive) structures. The following table breaks down these structures by type (caisson, well protector, or fixed platform). Consider the structure type and active status of one of these oil/gas structures.

Structure type

Caisson

Well protector

Fixed platform

Totals

Active

503

225

1447

2175

Inactive

598

177

450

1225

a. List the simple events for this experiment.

b. Assign reasonable probabilities to the simple events.

c. Find the probability that the structure is active.

d. Find the probability that the structure is a well protector.

e. Find the probability that the structure is an inactive caisson.

Working on summer vacation.Refer to the Harris Interactive(July 2013) poll of whether U.S. adults workduring summer vacation, Exercise 3.13 (p. 169). Recall thatthe poll found that 61% of the respondents work duringtheir summer vacation, 22% do not work at all while onvacation, and 17% were unemployed. Also, 38% of thosewho work while on vacation do so by monitoring theirbusiness emails.

a.Given that a randomly selected poll respondent will work while on summer vacation, what is the probability that the respondent will monitor business emails?

b.What is the probability that a randomly selected poll respondent will work while on summer vacation and will monitor business emails?

c.What is the probability that a randomly selected poll respondent will not work while on summer vacation and will monitor business emails?

The sample space for an experiment contains five sample points with probabilities as shown in the table. Find the probability of each of the following events:

a. Either 1,2 or 3 occurs

b. Either 1,3 or 5 occurs

c. 4 does not occur

Compute each of the following:

a.94

b. 72

c. 44

d. (50)

e.(65)

Working mothers with children. The U.S. Census Bureaureports a growth in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of mothers with infant children in the year 2014. (The numbers in the table are reported in thousands.) Consider the following events: A = {Mom with infant works}, B = {Mom with infant is married}. Are A and B independent events?

working

Not working

Married

6027

4064

No spouse

2147

1313

(Data from U.S. Census Bureau, Bureau of LabourStatistics, 2014 (Table 4).
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