A particular operation has six components. Each component has a success probability p = 0.8, independent of any other component. The operation is successful if both: • Components 1, 2, and 3 all work, or component 4 works. • Either component 5 or component 6 works. What is the probability that the operation is successful?

A particular operation has six components. Each component has a success probability p = 0.8, independent of any other component. The operation is successful if both: • Components 1, 2, and 3 all work, or component 4 works. • Either component 5 or component 6 works. What is the probability that the operation is successful?

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

Similar questions

A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (22)%, and (13)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2?
A circuit operates as long as there is a functional path, which does not include any dysfunctional (broken) switches on its path, between 1 and 2. The probabilities that the switches A, B, and Y are not functioning or broken (Failure, F) are 12%, (20+I)%, and (10+H)%, respectively (as shown in the figure below). The switches function independently. What is the probability that the circuit operates successfully (Success, S) from 1 to 2? H is 3 and I is 2
A jet fighter consists of two engines. The probability that the second engine functions in a satisfactory manner during its design life is 0.97, and the probability that at least one if the two engines does so is 0.975 and the probability that both engine do so is 0.93. Given that the first engine functions in a satisfactory manner throughout its design life, what is the probability that the second one also?
A manufacturing process produces, on the average, 3% defective items. The company ships 15 items in each box and wishes to guarantee no more than 1 defective item per box. If this guarantee accompanies each box, what is the probability that the box will fail to satisfy the guarantee?
Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10
The device consists of 3 elements. The probability of failure free operation of each of them are respectively equal to. 0.6, 0.7, 0.8. Find the probability that at least two of elements will work without fail.
Two machines turn out all the paper bags produced in the plant. Machine A produces 38% of the bags and machine B produces 62% of the bags. Machine A produces defective bags 1.9% of the time and machine B produces defective bags 3.8% of the time. Given a defective bag, what is the probability that it came from machine B?
Global Airlines operates two types of jet planes: jumbo and ordinary. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. Global serves two types of customers, business and tourist. Business customers are 70% of Global customers, while tourists make up 30%. 15% of Global's customers fly on jumbo jets and are tourists. What is the probability that a customer is a tourist and flies on a regular jet?
Answers must be in 4 decimals |1. Ben plans to enforce speed limits using radar traps at 4 different locations within the campus. The radar traps at each of the locations L1, L2, L3, and L4 are operated 40%, 30%, 30%, and 20% of the time, and if a person who is speeding on his way to work has probabilities of 0.2, 0.1, 0.5, and 0.2, respectively, of passing through these locations, what is the probability that he will not receive a speeding ticket? 2. Barangay Scout Fernandez has one fire truck and one ambulance available for emergencies. The probability that the fire truck is available when needed is 0.95, and the probability that the ambulance is available when called is 0.90. in the event that there is a fire in the barangay, find the probability that both the ambulance and the fire truck will be available.
At least one-half of an airplane's engines are required to function in order for it to operate. If each engine independently functions with probability p, for what values of p is a 4-engine plane more likely to operate than a 2-engine plane?
Which of the following expressions represents the number of distinguishable permutations of the letters of the word CONCLUSIONS? 11! 8! C. 11! 2! 2! 2! 2! 11! А. 11! В. С. D. 2! 2! 2!
A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?