The security system in a house has two units that set off an alarm when motion is detected. Neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. Suppose that for motion in a certain location, the probability that detector a goes off and detector b does not go off is 0. 25, and the probability that detector a does not go off is 0. 35. What is the probability that detector b goes off?.

Answers

Answer 1

The probability that detector B goes off is 0.75

The probability of an event is known to be the likelihood or chance for an event to occur.

From the given information let consider:

A = the time when detector A goes off, andB = the time when detector B goes off

Since one or both of them always goes off, then:

P(A or B) = 1

Their complements will be zero, i.e.

P(A' and B') = 0

Similarly, we are given that:

P(A and B') = 0.25

Then;

P(A') = 0.35

The set probability for A will be:

P(A) = 1 - P(A')

P(A) = 1 - 0.35

P(A) = 0.65

Finally, the probability that detector B goes off can be computed as:

P(B) = P(A) P(B|A) +P(A') P(B|A')

P(B) = P(A) (1 - P(B|A')) + P(A') (1 - P(B'|A')

[tex]\mathbf{P(B) = P(A) (1-\dfrac{P(A \ and \ B')}{P(A)}) +P(A') (1 - \dfrac{P(A' \ and B')}{P(A')})}[/tex]

[tex]\mathbf{P(B) = 0.65 (1-\dfrac{0.25}{0.65}) +0.35 (1 - \dfrac{0}{0.35})}[/tex]

P(B) = 0.75

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Related Questions

Mi padre y yo 1 of 2 (quitar) las cortinas y 2 of 2 (limpiar) las ventanas.

Answers

For the sentence to be grammatically correct, the verbs must be conjugated in the preterite tense as follows:

Mi padre y yo quitamos las cortinas y limpiamos las ventanas.

Translation: My father and I removed the curtains and cleaned the windows.

The preterite tense is a verb tense that is used to describe actions that occurred prior to the moment of enunciation.

The sentence "Mi padre y yo quitamos las cortinas y limpiamos las ventanas", describes actions performed in the past.

Therefore, we can conclude that the preterite tense is a verb tense that states an action that occurred in the past.

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The dewpoint is 15°c. What is the wet-bulb temperature on a sling psychrometer if the dry-bulb temperature is 18°c?.

Answers

Based on the information given, it should be noted that the wet-bulb temperature will be 16°C.

A psychrometer simply means a hygrometer that has two thermometers. In this case, one is hot while the other is moist and ventilated.

From the complete information, when the dewpoint is 15°c, the wet-bulb temperature on a sling psychrometer if the dry-bulb temperature is 18°c is 16°C.

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According to the graph, approximately how much of the us population used the internet in 2006? less than 20% about 40% about 70% more than 80%.

Answers

Answer:70%

Explanation:

C

“Finding information” tops the list of the most common reasons individuals use the internet, with nearly six in ten (58.4%) people globally citing it as such. Keeping in touch with friends and family comes in second place with 54.2 percent. Thus, option C is correct.

What US population used the internet in 2006?

Despite these advancements, the Report determines that 19 million Americans, or 6% of the population, still do not have access to fixed broadband service at threshold speeds. 14.5 million individuals, or close to one-fourth of the population, do not have access to this service in rural areas.

In America as a whole, 42% of adults had access to high-speed internet at home as of March 2006. Thirty percent of all adults accessed high-speed internet at home in March 2005. A rise in internet penetration from 66% to 73% over the previous year has contributed to this development in broadband adoption.

Therefore, According to the graph, approximately 70% US population used the internet in 2006.

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#SPJ5

Which three processes are involved when a multicellular organism reproduces sexually.

Answers

Answer:

mitosis. ,. meosis ,. formation of gamettes

Read the table of contents. The traveler’s guide to japan table of contents 1. Japan’s history: then and now…………. 3 2. Itineraries for must-see cities…………. 27 3. Getting around…………………………. 46 4. Basic greetings…………………………. 63 5. Traveling on a budget……………………89 in which chapter would a reader find the most helpful information about the different modes of transportation available in japan? chapter 2: itineraries for must-see cities chapter 3: getting around chapter 4: basic greetings chapter 5: traveling on a budget.

Answers

Answer:

Answer is Chapter 3.

Explanation:

The chapter that would be the most helpful to someone planning a trip to Japan is  a chapter on the types of accommodations available.

What is the book about?

The book on the traveler’s guide to Japan is known to be a book that talks about the planning of a trip to Japan and everything to know about it.

Note that by adding a chapter on the types of accommodations available in Japan, one can be able to known what kind of accommodations  use if one is planning a trip to that country.

See full question

If added to "The Traveler’s Guide to Japan,” which chapter would be the most helpful to someone planning a trip to Japan?

a chapter on the Japanese educational system

a chapter on the governing bodies in Japan

a chapter on the cultural influences of China

a chapter on the types of accommodations available

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Listen to the audio and then answer the following question. Feel free to listen to the audio as many times as necessary before answering the question. What are the family plans for sunday evening?.

Answers

Answer:

gathering with relative and friends

On a small planet, an astronaut uses a vertical force of 175 newtons to lift an 87. 5-kilogram boulder at constant velocity to a height of 0. 350 meter above the planet’s surface. What is the magnitude of the gravitational field strength on the surface of the planet?.

Answers

Since the boulder is raised with constant velocity, the net force on the boulder is zero, so that the boulder has weight 175 N on this planet. If its mass is 87.5 kg, then the acceleration due to gravity is g such that

175 N = (87.5 kg) g   ⇒   g = (175 N) / (87.5 kg) = 2.00 N/kg = 2.00 m/s²

Decide if por or para should be used in the following sentence. Ella es muy extrovertida _____ una chica tímida. Por para.

Answers

The correct option is Ella es muy extrovertida para una chica tímida.

Por and para are two Spanish prepositions, but they are used differently.

When to use por?

We use por when we talk about

Why something happened To mention who did something. For example, la comida fue hecha por el John.

When do we use para?

We use para when:

We want to talk about the what.We are using adjectives to talk about someone or something and making comparisons.

In conclusion, as the sentence is talking about the characteristics of a girl and making a comparison, the correct word is para.

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Answer:

para

Explanation:

What is 3x3 – 11x2 – 26x + 30 divided by x – 5? 3x2 – 4x + 6 3x2 + 4x – 6 3x2 + 26x + 8 3x2 – 26x + 8.

Answers

First question answer is -26x + 17
x - 5

The height of a stack of dvd cases is proportional.

Answers

Well in the sense that the stack is stacked nicely yes

Which item(s) will require a journal entry to update the balance in the cash account?.

Answers

Examples of items requiring a journal entry as the result of the bank reconciliation include:

Bank service charges which are often shown on the last day of the bank statement. ...

Check printing charges.

Customer checks that were deposited but are now returned as NSF (not sufficient funds)

Bank fees for returned checks.

Which event organized peace between germany and the allied forces at the end of world war i?.

Answers

Answer:

Treaty of Versailles

Explanation:

it was signed in June 1919

it was signed by Germany France UK and some other countries as well

Which of the following is not considered a potential insider threat indicator.

Answers

There are different kinds of potential insider threat indicators. The option that is not considered a potential insider threat indicator is New interest in learning another language

The Indicators of a potential insider threat are divide into different categories. They are known to be the indicators of:

RecruitmentInformation collectionInformation transmittal General suspicious behavior

People are often interested in learning another language. The study of foreign languages helps us greatly as it teaches and encourages one to respect other people.

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According to the age of revolution tab, who were the shakers, and what was one of their influences in this era of music?.

Answers

This answer is in here can you please give me the brainiest question. Look at the picture for the answer

If $535 is invested at an interest rate of 6% per year and is compounded continuously, how much will the investment be worth in 10 years? use the continuous compound interest formula: a = pert $1307. 12 $974. 83 $973. 38 $403. 43.

Answers

The Amount of investment equals $974.83.

The continuous compound interest helps to calculate an investment that are reinvested into the balance over a infinite number of periods.

The formula for continuous compound interest is A=P^e^(r*t)

Amount of investment = $535 * e^(6%*10)

Amount of investment = $535 * 1.82211880039

Amount of investment = $974.833558209

Amount of investment = $974.83

Therefore, the Option B is correct since the Amount of investment equals $974.83.

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Which term refers to a secure systems ability to protect against.

Answers

Answer:

Hey mate!

Explanation:

Integrity refers to the protection of information from unauthorized modification or destruction. Ensuring integrity is ensuring that information and information systems are accurate, complete and uncorrupted.

pls mark me as brainliest!!

Read the writers original draft of this sentence from paragraph 4.

Answers

Answer:

Can you please post a picture for the sentence??

Based on the passage, what type of literature is beowulf? which of these lines from the poem describes beowulf?.

Answers

Based on the passage, the lines from the poem describes beowulf is mighty and noble.

According to the question, we are to discuss the poem beowulf and the line that describes this poem.

As a result of this we can see that this poem Gredel which was evil moster was defeated by King of denmark and a beowulf.

Therefore, lines from the poem that describes beowulf is mighty and noble.

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List the angles of ∆ abc from smallest to largest. Ab = 20, bc = 12, ca = 10.

Answers

The angle of the triangle ABC from smallest to largest are approximately 22°, 27° and 131°.

The sides of the triangle are as follows;

AB = 20

BC = 12

AC = 10

Let's find ∠A using cosine rule,

a² = b² + c² - 2bc cos A

cos A = b² + c² - a² / 2bc

Therefore,

cos A = 10² + 20² - 12²  / 2 × 10 × 20

cos A = 100 + 400 - 144 / 400

cos A = 356 / 400

cos A = 0.89

A = cos⁻¹ 0.89

A = 27.1267531173

∠A ≈ 27°

Using sine rule let's find ∠B

12 / sin 27 = 10 / sin B

cross multiply

12 sin B = 10 sin 27

sin B = 10 sin 27 / 12

sin B = 10 × 0.45399049974  / 12

sin B = 4.5399049974  / 12

B = sin⁻¹ 0.37832541645

B = 22.2299936087

∠B = 22°

Using sum of triangle theorem let's find ∠C

∠C = 180 - 27 - 22

∠C = 131°

The angles from smallest to largest are approximately 22°, 27° and 131°.

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there are 80 students in a school. every student is taking

Answers

Answer:

then you are single it every one taken

In the middle of our sleep a burglar broke in our house.

Answers

The question requires that we identify the past continuous form of the sentence. The answer to the question will be:

When we were in the middle of our sleep, a burglar broke into our house.

The past continuous form of a sentence describes an action that started sometime in the past and continued for a while after it began.

The sentence above describes a past continuous sentence because it described an action that was ongoing sometime in the past.

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Education empowers a person elaborate this statement with example.

Answers

Answer:

Education empowers a person by creating more employment opportunities, securing a higher income, developing problem-solving skills, and by providing a a prosperous happy life.

Explanation:

Education empowers a person by opening doors to the job market, combating inequality, fostering solidarity, and promoting environmental stewardship. Education empowers people with the knowledge, skills and values they need to thrive and build a better world.

Which of the following statements correctly explains the tectonic plate activity on the west coast of the united states?.

Answers

The statement which correctly explains the effect of tectonic plate activity on the west coast of the United States of America is that: Earthquakes occur at the San Andreas Fault when stored energy is released from locked plates.

A tectonic plate is also known as lithospheric plate and it can be defined as an enormous, solid, irregularly shaped rock slab, that is made up of two (2) main plates:

Oceanic platesContinental plates

According to the theory of plate tectonics, the arrangement of continents, oceans, volcanic activity, earthquakes, and the formation of landforms such as mountains, are caused by the movement of tectonic plates over millions of years.

In this context, the effect of tectonic plate activity on the west coast of the United States of America is that earthquakes would take place at the San Andreas Fault when the energy stored in locked plates are released, as shown in the image attached.

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Which of the following is not one of the big five personality dimensions.

Answers

Answer:

Dependency

Explanation:

Dependency is not included in the Big five Model

Which set of word clues best helps the reader to determine what the character is like?.

Answers

Answer:

What character? there's no pic of the context ur asking for

Layla has a coin that has a 60\%60%60, percent chance of showing heads each time it is flipped. She is going to flip the coin 555 times. Let xxx represent the number of heads she gets. What is the probability that she gets more than 333 heads?.

Answers

The probability that she gets more than 3 heads is 0.3456.

There are only two possible outcomes for a fliped coin, either it is head, or it is tail. Since the result is independent of each other coins, the binomial distribution will be used.

Given the following parameters:  

x is the number of successes = 5 (coin flipped 5 times) n is the number of trials p is the probability of success on a single trial = 0.6

Using the binomial distribution formula:

[tex]P(X =x)=nC_x p^x (1-p)^{n-x}\\P(X =3) = 5C_3 \ (0.6)^3 (1-0.6)^{5-3}\\P(X =3) = 5C_3 \ (0.6)^3 (0.4)^{2}\\P(X=3)=0.3456[/tex]

Hence the probability that she gets more than 3 heads is 0.3456.

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Answer:

0.34 is the correct answer on khan

Explanation:

what is the kinetic energy of a 4 kg cart pushed at a rate of 0.5 m/s?

Answers

Answer:

2 N/newtons of force

Explanation:

2kg x 0.5m/s/s = 2 N/newtons of force

If the speaker says, "we’re gonna go to paris in a few days, um, then we’re off to venice," you would caption it this way:.

Answers

The way the given speech could be captioned is that; We’re going to go to Paris in a few days, then we’re off to Venice.

From the given speech of the speaker, we can see that it is a direct speech as the exact words he used and the other words are all quoted in inverted commas.

Whereas, In indirect speech, the exact words used by the speaker are not quoted.

The best way to caption the speech is that the inverted commas will removed as well as well as the conjunction used and we will make it an indirect speech as follows;

We’re going to go to Paris in a few days, then we’re off to Venice.

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client quietly paces in the ed waiting area with his hands on his hips and rubbing his mid-lower left side. he has a flat facial expression. which factor is most important for the nurse to consider when interpreting this client’s pain behavior?

Answers

The most important factor to consider for a nurse when interpreting this client’s pain behavior is the client's cultural identity. This issue is fundamental for providing good healthcare services.

The client's cultural identity refers to the systems of beliefs and moral values of the society in which a patient (client) developed.

The client's cultural identity represents a fundamental aspect when providing healthcare services.

Cultural identity may or not include issues associated with sexual orientation, identity, economic status, religion, etc.

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According to the university of michigan studies, leaders who are production oriented are described as emphasizing interpersonal relationships and as taking a personal interest in the needs of their followers.

Answers

The statement which states that according to the University of Michigan studies, leaders who are production oriented are described as emphasizing interpersonal relationships and as taking a personal interest in the needs of their followers is FALSE.

A leader is a person who is in charge of a group of people and is tasked with showing them how things are done and for them to also follow his instructions and trust his leadership.

With this in mind, we can see that the above statement about the research which was made in the University of Michigan is FALSE because production oriented leaders are not described as emphasizing interpersonal relationships.

Therefore, the correct answer is FALSE

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Other Questions
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Lost and out of food, he feared he had but a few hours before darkness closed in, trapping him in the bitter cold with the creatures of the night.He closed his eyes to fight back tears, when he heard it in the distance. Water! His fathers words came flowing into his mind; one tip he actually remembered. If youre ever lost, find a river and follow it.In a flash, he was on his feet, scaling fallen trees, tearing through brush, frantically following the sound. The sky grew darker, but the noise grew louder, and Randall, tired and scared, forged ahead until he found it. He reached the river bank and was mulling his next move when a sudden splash caught his eye.A majestic eagle rose from the water, soaring skyward with a freshly caught fish in its talons. Could it be the same eagle nested above his camp? It glided triumphantly into a high nest a short distance away, eager to greet its family. 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