Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q. 89. (page 334)

Merry and bright? A string of Christmas lights contains 20 lights. The

lights are wired in series so that if any light fails, the whole string will go dark. Each light has probability 0.98 of working for a 3-year period. The lights fail independently of each other. Find the probability that the string of lights will remain bright for 3 years.

Short Answer

Expert verified

The required probability is0.6676

Step by step solution

01

Given information

Given that,

Probability of success (p)=0.98

The failure of light is unrelated to the failure of other lights.

02

Calculation

The probability that the string of lights will remain lit for three years is calculated as follows:

P(Lightswillbebrightfor20years)=(0.98)20 =0.6676

Therefore, the required probability is0.6676

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

2Drive to exercise : The two-way table summarizes the responses of 120 people to a survey in which they were asked, “Do you exercise for at least 30 minutes four or more times per week?” and “What kind of vehicle do you drive?”

ExerciseSedanSUVTruck
Yes251512
No202424

Suppose one person from this sample is randomly selected.

a. Find the probability that the person drives an SUV.

b. Find the probability that the person drives a sedan or exercises for at least 30 minutes four or more times per week.

c. Find the probability that the person does not drive a truck, given that she or he exercises for at least 30 minutes four or more times per week.

Waiting to park Do drivers take longer to leave their parking spaces when

someone is waiting? Researchers hung out in a parking lot and collected some data. The

graphs and numerical summaries display information about how long it took drivers to

exit their spaces.

a. Write a few sentences comparing these distributions.

b. Can we conclude that having someone waiting causes drivers to leave their spaces more

slowly? Why or why not?

If a player rolls a 2,3,or12, it is called craps. What is the probability of getting craps or an even sum on one roll of the dice?

a. 4/36

b. 18/36

c. 20/36

d. 22/36

e. 32/36

Mystery box Ms. Tyson keeps a Mystery Box in her classroom. If a student meets expectations for behavior, she or he is allowed to draw a slip of paper without looking. The slips are all of equal size, are well mixed, and have the name of a prize written on them. One of the “prizes”—extra homework—isn’t very desirable! Here is the probability model for the prizes a student can win:

a. Explain why this is a valid probability model.

b. Find the probability that a student does not win extra homework.

c. What’s the probability that a student wins candy or a homework pass?

An unenlightened gambler

a. A gambler knows that red and black are equally likely to occur on each spin of a

roulette wheel. He observes that 5 consecutive reds have occurred and bets heavily on

black at the next spin. Asked why, he explains that “black is due.” Explain to the

gambler what is wrong with this reasoning.

b. After hearing you explain why red and black are still equally likely after 5reds on the

roulette wheel, the gambler moves to a card game. He is dealt 5straight red cards from

a standard deck with26red cards and 26black cards. He remembers what you said and

assumes that the next card dealt in the same hand is equally likely to be red or black.

Explain to the gambler what is wrong with this reasoning.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free