An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activa correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 98.765). (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 98.76). (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.92?

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activa correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently. (a) What is the probability that all of the sprinklers will operate correctly in a fire? Round your answer to three decimal places (e.g. 98.765). (b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire? Round your answer to two decimal places (e.g. 98.76). (c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.92?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: Your friend is attempting 10 free throws, and from experience, you know that your friend’s…

A: The random variable X is defined as the number of free throws which follows binomial distribution…

Q: A drawing class was assigned a final project where students had to choose one art medium and one…

Q: The probability that event A occurs is 1/5, the probability that event B occurs is 3/4 and the…

Q: Evie was doing an experiment for her biology class. She determined that if she randomly selected a…

A: Given that, Probability ( Brown hair), P(BH)= 0.5 Probability (Blue eyes), P(BE)= 0.57 And…

Q: On a particular manufacturing job, the probability that there will be a shortage of copper is 0.37.…

A: Solution: Let A be the event that shortage of copper and B the event that shortage of aluminium.…

Q: The probability that it will rain on a given day is 0.23. What is the probability that it will not…

A: The probability that it will rain on a given day is 0.23 P(Rain) = 0.23 We know that , complement of…

Q: If the probability that an event does no occur is 0.3 determine the probability that the event…

Q: Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if Bob goes…

A: Given, Suppose that the probability that Bob will go downtown is 45%. Now, also suppose that if…

Q: The probability that a student pilot passes the written test for a private pilot's license is 0.55.…

A: Probability distributions are of two types, discrete and continuous distributions. Binomial…

Q: The mean percent of childhood asthma prevalence in 43 cities is 2.18%. A random sample of 33 of…

A: The sampling distribution of the mean childhood asthma prevalence will follow normal distribution…

Q: The average number of field mice per acre in a 5-acre wheat field is estimated to be 10. Find the…

A: Let X be the number of mice. The average number of field mice per acre is estimated to be 10.

Q: 20% of all people are O negative. If 12 people donate blood at the blood drive 1. The probability…

Q: A person died prematurely, find the probability with which he could have been a heavy smoker given…

A: Step 1:First, we define the events:D: The person died prematurelyH: The person is a heavy smokerL:…

Q: A recent survey in Montana revealed that 20% of the vehicles traveling on highways, where speed…

A: From the provided information,Probability of the vehicles travelling on highways, where speed limits…

Q: The probability that Aiko can drive to work without having to stop at a red light is 0.125. The odds…

A: Given: The probability of not having to stop at a red light is: P(Not Stop) = 0.125

Q: in a box of pens and pencils, the probability of randomly choosing a sharpened pencil is 0.54 and…

Concept explainers

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.

Question

An article in Fire Technology, 2014 (50.3) studied the effectiveness of sprinklers in fire control by the number of sprinklers that activate correctly. The researchers estimate the probability of a sprinkler to activa
correctly to be 0.7. Suppose that you are an inspector hired to write a safety report for a large ballroom with 10 sprinklers. Assume the sprinklers activate correctly or not independently.
(a) What is the probability that all of the sprinklers will operate correctly in a fire?
Round your answer to three decimal places (e.g. 98.765).
(b) What is the probability that at least 7 of the sprinklers will operate correctly in a fire?
Round your answer to two decimal places (e.g. 98.76).
(c) What is the minimum number of sprinklers needed so that the probability that at least one operates correctly is at least 0.92?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Conditional Probability, Decision Trees, and Bayes' Theorem$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

The probability of a thunderstorm on Memorial Day is 0.13 and the probability of a thunderstorm on Independence Day is 0.59. Assuming that these two are Independent, what is the probability of thunderstorms on both Memorial and Independence Day?
On the first day of music class, students submitted a survey. One survey question asked students to report which music genre they prefer. Another question asked students how frequently they sing in the shower. The probability that a student prefers metal is 0.7, the probability that a student sings in the shower 1-2 times a week is 0.4 and the probability that a student prefers metal and sings in the shower 1-2 times a week is 0.3. What is the probability that a randomly chosen student prefers metal or sings in the shower 1-2 times a week?
A study tracked a large group of people for 10 years. At the start of the study, 20% were heavy smokers (H), 30% were light smokers (L), and 50% were non-smokers (N). The interest of the study was whether the people in the study died during the study (D) or not die (Dc ). The probability that a light smoker died during the study was twice that of the probability of a non-smoker dying. Also, the probability that light smoker died during the study was half that of the probability of a heavy smoker dying. A randomly selected person from the study died during the study. What is the probability that this person was a heavy smoker (given they died, what is the probability they were a heavy smoker H)?
The probability that a statistics graduate from a Canadian university gets a data science job is 0.6.Ten graduates applied for executive jobs.What is the probability that exactly 3 will get jobs, at least 2 will get a job, at most 8 will get a job, and no one will get a job?