The probability that machine A will be perform-ing a usual function in 5 years’ time is 1/4 while the probability thatmachine B will still be operating usefully at the end of same periodis 1/3.Find the probability that in five years' time :(a) both machines will be performing a usual function,(b) neither will be operating,(c) only machine B will be operating, and(d) at least one of the machines will be operating.

Here Given two machines A and B And Probability their preforming usual in 5 years time…

Find the probability that in five years' time : (a) both machines will be performing a usual function, (b) neither will be operating, (c) only machine B will be operating, and (d) at least one of the machines will be operating.

Find the probability that in five years' time : (a) both machines will be performing a usual function, (b) neither will be operating, (c) only machine B will be operating, and (d) at least one of the machines will be operating.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.2: Probability

Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...

See similar textbooks

Related questions

Q: : Construct the table representing the Probability Mass Function of P(X = x). %3D x 1, 2,4 P(X = x){...

A: given ; P(X=x)=15x=1,2,425x=3 0otherwise

Q: Which among the value is approximately equal to P(0.99<Z<1.5) A.) 0.0943 B.) 0.2333 C.) 0.7333 0.772...

A: which among the value is approximately equal to P(0.99<z<1.5)

Q: Sample size 9 whose data are given below is drawn from a population having a mean = 8 and standard d...

A: Mean of sampling distribution, Then x̄= ΣXi/n =(11+5+7+11+10+13+13+11+9)/9 =10

Q: How many different arrangements of 4 letters can be formed if the first letter must be W or K (repea...

A: Total no.of letters(A to Z)=26

Q: An event B has probability 0.6. If A and B are An event A has probability 0.7. independent, which of...

Q: Specifically, we see from model selection that it may be desirable to select only a subset from avai...

A: Given information: The number of observations is n. The number of predictor variables is n – 1.

Q: 2. You form a seven-digit code using the digits 0, 1, 1, 2, 3, 4, 5. What are the chances that the n...

A: Given : Using digit 0,1,1,2,3,4,5 we form 7 digit code . We need to find the chances that the numb...

Q: Which among the value approximately equal to P(Z>-1.20) A.) 0.1151 B.) 0.3849 C.) 0.7698 D.) 0.8849

A: Let Z be the random variable from normal distribution the we will find the probability P(Z> -1...

Q: 6 - How many different two-letter passwords can be formed using the letters A, B, C, D, E, and F if ...

A: given letters A B C D E F total no. of letters = 6 we need a two letter password

Q: Select your answer- C. Consider the required conditions for a discrete probability function, shown b...

A: Given that, A technician services mailing machines at companies in the Phoenix area. Depending on th...

Q: (a) both machines will be performing a usual function, (b) neither will be operating, (c) only machi...

A: Here use venn diagram Here A = machine A operate usually B = machine B operate usually

Q: the probability that he fails the short exam with a passing rate of 50% and will only have 10 questi...

A: Here Given Mark decided to take short exam which has 10 Questions and each has 4 possible answers.

Q: Let A, A2,., A, be n mutually exclusive and exhaustive fined on a sample space S and let H be an arb...

Q: A drum contains 4 black balls, 5 red balls and 6 green balls. If 5 balls are selected at random, fin...

Q: 2 What fiaction of these palls trave stripes 34

A: Given that Stripes ball=2 Star ball=2 Doted ball=2

Q: Let X Poisson(A) and Y = VX. Use the delta method to approximate the mean and variance of Y.

Q: on 16.47. A total of 100 people was surveyed. 60 of them were smokers-40 being male and 20 being fem...

Q: If a real estate office sells 1.6 houses on an average weekday and sales of houses on weekdays are P...

A: As per our guidelines we can solve first three sub part of question and rest can be reposted. Soluti...

Q: The joint probability mass function of the two random variables (X, Y) is given by f(x,y) = { 1/5(3...

A: INTRODUCTION: Let X and Y be two discrete random variables. Then the two random variables X and Y a...

Q: . Suppose that the joint p.m.f of X and Y is modeled as fx (x, y) = s(x + y), x = 1, 2, 3 and y =1, ...

A: It is given that The joint PMF of random variables X and Y is f(x, y) = c(x + y), x = 1,2,3 and y = ...

Q: In a commercial survey involving 1000 person on brand preference, 120 were found to prefer brand X o...

A: Let X=number of persons who have no brand preferences. Given: X only=120 Y only=200 Z only=150 X or ...

Q: Statistical economics: A committee of 4 people is to be appointed from 3 officers of the production ...

Q: A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the pro...

A: if a number cub is rolled and a coin is tossed than the possible outcomes are1,T1,H2,T2,H3,T3,H4,T4,...

Q: The table displays the number and type of tickets bought for a play that was performed in both the a...

A: Let A represents 'a child tickets is bought for a play' and B represents 'the play is performed in t...

Q: The probability distribution for the number of students in Statistics classes offered at a small col...

Q: How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6, and 9.

A: Given: Using the digit 2,3,4,5,6 and 9 We need to find how many four digit odd number be formed l...

Q: A lot containing 7 components is sampled by o quality inspector. The lot contains 4 good components ...

Q: which Store has greatest average number of tablet sold? which Store has least avernge number tablet ...

A: We have given that the probability distribution of three different stores and their mean & varia...

Q: - It is equally probable that the pointer on the spinner shown will land on any one of the eight reg...

A: Let A be the event that points stops at even number Therefore, A = { 2, 4, 6, 8} And B the event th...

Q: box contains 17 transistors, 4 of which are defective. If 4 are selected at random, find the probabi...

A: A box contains 17 transistors, 4 of which are defective. If 4 are selected at random, we know , out...

Q: Show complete solution A.) A woman has 16 close friends. Find the number of ways she can invite 8 o...

A: Given Number of close friends=16 Invite 8 out of 16

Q: Theorem 2.1.5 If A1, A2 ..., An are n (2 2) events, then P U A; |- £ P(A;} – E P(A;N Aj) + £ P(A¡ N ...

Q: A random variable X follows normal distribution with the mean 100 and standard deviation 4. Find the...

Q: A pair of dice is rolled and the sum is determined. Let the random variable x denote this sum. What ...

A: Let S be the sample space E1 be the event for getting sum 5 E2 be the event getting sum 6 E3 be t...

Q: What is the probability of rolling, on a fair dice a multiple of 3 given that an even number was dra...

A: We have given that The sample space is S = { 1, 2, 3, 4, 5, 6 }.The total number of outcomes = 6 ...

Q: Exercise 4.3 Two measurement methods are used to evaluate the surface smoothness of a paper product....

Q: A box contains 9 plain pencils and 1 pen. A second box contains 3 color pencils and 3 crayons. One i...

A: From the given option we have In first box total items = 9+1 = 10 In second box total items = 3 +3 =...

Q: A consumer products company is formulating a new shampoo and is interested in foam height (in millim...

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted.... ...

Q: Consider a political discussion group consisting of 8 Democrats, 10 Republicans, and 2 Independents....

Q: 11.43. The number (x) of items of a certain kind demanded by customers follows the Poisson law with ...

Q: elved are tracked using sortware that can tell the e-mali sender when, where, and on what type of de...

Q: Consider the probability that a random interval x + (t.05)S will contain the fixed (population mean)...

A: The given information is- Sample size = n = 10 Sample mean = x̄ = 131 Sample Variance = s2 = 971.11 ...

Q: In a certain population, it is given that 10% of the people weigh less than 41 kg and 30% of the peo...

A: Let a random variable X denotes the weight of the people. Let μ and σ be the true mean and the stan...

Q: A production process manufactures electronic components with timing signals whose duration follows a...

A: Here we have given that X ~ N (µ, σ )

Q: Exercise 5.6 The number of cracks that need repair in a section of interstate highway follows a Pois...

A: The number of cracks that need repairs in a section of interstate highway follows a Poisson distribu...

Q: A memory test consists of 35 tasks. Each task is graded on a scale of 1 to 10. The score on the memo...

A: here given, mean = 5.1 standard deviation =3 x= score on memory test

Q: Explain the Figure below

A: Given information: A bar graph of price and transition probability is given.

Q: (a) P(C|A) (b) P(B|A N B) (C) P(B|A U B)

A: Note: Hi, thank you for the question. As per our company guideline we are supposed to answer only fi...

Q: The Joint probability distribution of X and Y is given below: Y 0.4 0.1 1. 0.2 0.3 Find the correlat...

Q: Someone wants to know how many different outfits they can make with 3 coats, 5 pants, 7 shirts, and ...

Question

The probability that machine A will be perform-
ing a usual function in 5 years’ time is 1/4 while the probability that
machine B will still be operating usefully at the end of same period
is 1/3.
Find the probability that in five years' time :
(a) both machines will be performing a usual function,
(b) neither will be operating,
(c) only machine B will be operating, and
(d) at least one of the machines will be operating.

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the conditional probability of the event E, getting a six, given that the event F, getting an even number, has occurred is P(EF)=___________.
Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Suppose the probability that a particular computer chip fails after a hours of operation is 0.00005∫_a^∞ e^{−0.00005t}dt.Of the chips that are still operating after 15,000 hr, what fraction of these will operate for at least another 15,000 hr
Suppose that an average of 30 customers per hour arrive at Shwapno and the time between arrivals is exponentially distributed. a. On average, how many minutes elapse between two successive arrivals? b. After a customer arrives, find the probability that it takes more than 8 minutes for the next customer to arrive. c. After a customer arrives, find the probability that it takes less than 2 minutes for the next customer to arrive. d. 70% of the customers arrive within how many minutes of the previous customer? e. Which is larger, the mean or the median?
Suppose 5 students are going to take a test independently from each other and that the number of minutes that any student needs to finish the exam has an exponential distribution with mean 80.If the test starts at 9 a.m., determine the probability that at At least one of the students finishes the exam before 9:40 am.
In a certain year,27% of adults in a certain country viewed a college education as essential for success. For the following ten-year period, this percentage increased by approximately 2.6percent each year. The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by ________.
A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the probability (two decimal place accuracy) that he finds less than 12 bears in a given 2 square mile region of the park?
Suppose that there are two identically-looking batteries in a box. The first one should last for a time that is exponentially distributed with parameter λ1 = 1 (in months). The second one should last for a time that is exponentially distributed with parameter λ2 = 2. A battery has been picked randomly and is still working after two months. Given this information, what is the probability that the first battery was picked?
Suppose that the probability of a hurricane striking a state in any single year is 1 in 10 and that this probability has been the same for the past 1000 years. Which of the following is implied by the law of large numbers? A) The state has been hit by close to (but not necessarily exactly) 100 hurricanes in the past 1000 years because as the years increase, the closer the proportion of hurricanes should be to 0.1. B) If no hurricanes have hit the state in the past 10 years, then the probability of a hurricane hitting next year is greater than 0.1 because the state is due for a hurricane. C) The state has been hit by close to (but not necessarily exactly) 100 hurricanes in the past 1000 years because as the years increase, the proportion of hurricanes that hit the state should decrease. D)The state has been hit by exactly 100 hurricanes in the past 1000 years because 100 is how many times the state was expected to be hit by hurricanes. E) If no hurricanes have hit the…
Prove that for a timelike interval, two events can never be considered to occur simultaneously.
The U.S. Bureau of the Census prediction for the percentage of the population 65 years and older can be modeled as p(x) = −0.00022x3 + 0.014x2 − 0.0033x + 12.236 percent where x is the number of years since 2000, data from 0 ≤ x ≤ 50. 1. Determine the value of x in the domain 0 ≤ x ≤ 50 for which the percentage is predicted to be increasing most rapidly (Round your answer to three decimal places). 2. Thus, in which year is the percentage is predicted to be increasing most rapidly? 3. Calculate the percentage at that time. (Round your answer to two decimal places.) 4. Calculate the rate of change of the percentage at that time. (Round your answer to three decimal places.)
Two drunk start out together at the origin, each having the equal probability of making a step to the left or right along the x-axis. Assume that men make their steps simultaneously. Let N be the total number of steps taken by each man. Assume that a particular instant, they are separated by some distance. In this situation, in a given particular step. If they move towards each other, the separation between them decreases. If the move away from each other, the separation between them increases If they move in the same direction, the separation remains unaltered Then calculate (a) The probability of decreasing their separation (b) The probability of increasing their separation (c) The probability of no separation between them Out of N steps, n1 steps belong to decreasing the separation of them; n2 steps belong to increasing the separation of them and n3 steps belong to no separation. Then, calculate the following. (d) The probability of taking the steps n1, n2 and n3 (e) The…