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Chapter 3: Q106SE (page 204)

Condition of public school facilities. The National Center for Education Statistics (NCES) conducted a survey on the condition of America’s public school facilities. The survey revealed the following information. The probability that a public school building has inadequate plumbing is .25. Of the buildings with inadequate plumbing, the probability that the school has plans for repairing the building is .38. Find the probability that a public school building has inadequate plumbing and will be repaired.

Short Answer

Expert verified

The probability is 0.095.

Step by step solution

01

Important formula

The formula is P(A∩B)=P(A).P(B|A).

02

The probability that a public school building has inadequate plumbing and will be repaired.

Here, P(G)=0.25=chances of having inadequate plumbing.

P(F|G)=0.38= The school has plans to repair it.

P(G∩F)=P(G)×P(F|G)=(0.38)(0.25)=0.095

Therefore the probability is 0.095.

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Most popular questions from this chapter

An experiment results in one of three mutually exclusive events, A, B, or C. It is known that P (A)= .30, P(B)= .55 , and P(C)= .15. Find each of the following probabilities:

a. P(A∪B)

b.P(A∩C)

c. P (A/B)

d. P(B∪C)

e. Are B and C independent events? Explain.

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).

Working on summer vacation. Is summer vacation a break from work? Not according to a Harris Interactive (July 2013) poll of U.S. adults. The poll found that 61% of the respondents work during their summer vacation, 22% do not work while on vacation, and 17% are unemployed. Assuming these percentages apply to the population of U.S. adults, consider the work status during the summer vacation of a randomly selected adult.

a. What is the Probability that the adult works while on summer vacation?

b. What is the Probability that the adult will not work while on summer vacation, either by choice or due to unemployment?

In a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs only, 20 with wheels only, 8 with both legs and wheels, and 15 with neither legs nor wheels. One of the 106 social robots is randomly selected and the design (e.g., wheels only) is noted.

  1. List the sample points for this study.
  2. Assign reasonable probabilities to the sample points.
  3. What is the probability that the selected robot is designed with wheels?
  4. What is the probability that the selected robot is designed with legs?

A pair of fair dice is tossed. Define the following events:

A: [Exactly one of the dice shows a 1.]

B: [The sum of the numbers on the two dice is even.]

a. Identify the sample points in the events A,B,A∩B,A∪B,andAc.

b. Find the probabilities of all the events from part a by summing the probabilities of the appropriate sample points.

C. Using your result from part b, explain why A and B are not mutually exclusive.

d. Find P(A∪B) using the additive rule. Is your answer the same as in part b?
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