What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period?

What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period?

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: Suppose that A and B are two events for which P(A)=0.26, P(B)=0.76, and P(B|A)=0.51. Find each of…

Q: If A and B are events such that P(A)equals=0.60 and P(A∪B)equals=0.70, find P(B) when (a) A…

A: (a)If events A and B are mutually exclusive events, then, P (A or B) = P(A)+ P(B).Or, P(B) = P (A or…

Q: Suppose that 30% of applicants for an industry job are proficient at object-oriented programming…

A: It is given that: Probability that the candidate is proficient at OOP =310

Q: Tom, Mike and Jane decode the code independently, the probabilities of their successfully decoding…

A: Here, given that three people decide the code independently and the probabilities of each event is…

Q: If A and B are events with P(A)=0.6, P(A OR B)=0.98, P(A AND B)=0.02, find P(B).

Q: A family has three children, eacher of whom is a boy or a girl with probability 1/2. Let A = "there…

A: (a). Ans :- A and B are independent. Explanation :- Given that, The family has 3 childrens. i.e…

Q: Suppose we have three events A, B, and C. If P(A) > 0, P(B) > 0 and P(C) < 1, and we know that if…

Q: Suppose that AA and BB are two events for which P(A)=0.32P(A)=0.32, P(B)=0.73P(B)=0.73, and…

A: Given that : P(A)=0.32 P(B)=0.73 and P(B|A)=0.37 By using the properties of basic and…

Q: Define A, P(A) = 0.30, P(B) = 0.20, P(C) = 0.90 P(ANB) = 0.06, P(ANC) = 0.27, P(BOC) = 0.18,…

A: Given that P(A) = 0.30, P(B) = 0.20, P(C) = 0.90 P(A n B) = 0.06, P(A n C) = 0.27, P(B n C) = 0.18,…

Q: Let A and B be independent events with P(A) = P(An B) = P(AUB) = 1 ·|6 1 and P(B) = Find P(An B) and…

Q: Suppose A and B are events with P(A) = 0.25, P(B) = 0.64, and P(AUB) = 0.73. Then A and B…

A: Independent events : Let A and B be two events then the events are said to be independent if the…

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A: As per guideline expert have to answer first three subparts only.

Q: Let A and B be independent events with P(A) " and P(B) =. Find P(AN B) and P(A U B).

A: Given that P(A) = 1/8 P(B) = 1/5

Q: A recent census found that 51.9% of adults are female, 10.4% are divorced, and 5.9% are divorced…

A: Let F be the event that the person is femaleD be the event that the person is divorced.

Q: If A denotes some event, what does A denote? If P(A) = 0.008, what is the value of P(A)? What does A…

A: Given data: If A denotes some event, what does A' denote? If P(A) = 0.008, To find: what is the…

Q: Let A and B be events such that P(A)=1/4, P(A or B)=1/3, and P(A and B)=1/5. DetermineP(B)

Q: Shannon owns two stocks: A and B. The probability that A will be profitable is 0.7. The probability…

Q: For two events, A and B, we have P(A) = 0.8, P(B) = 0.7, and P(AUB) = 0.9. Then, the value for P(BA)…

A: Given that P(A) = 0.8, P(B) = 0.7, and P(A U B) = 0.9.

Q: Suppose that A and B are two independent events for which P(A) = 0.17 and P(B) = 0.59 Find each of…

A: For the given data Find p(A/B ) =? P(B/A) =? P( A and B ) =? P (A or B ) =?

Q: a) Show that for any three events A, B, and C, the probability that at least one of them occurs is…

A: Given We need to prove that for three events A,B and C,the probability that atleast one of them…

Q: Suppose that A,B, & C are three independent events such that Pr(A)=1/4, Pr(B)=1/3, and Pr(C)=1/2. A.…

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

Q: Suppose that A and B are events for which Р(A| B) — 0.8, Р(В A) — 0.15, and Р(A) — 0.2. P(B) =

Q: Let A and B be two events such that 0 < P(A) < 1. If P(B|A) = P(B|Ac), prove mathematically (not…

A: Given that A and B be two events such that 0 < P(A) < 1. If P(B|A) = P(B|Ac), We have to prove…

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any question so I am solving…

Q: Let A and B be events such that P(A) = 0.6, P(B) = 0.5and P(A∪ B) = 0.8.Find P(A B)). Are A and B…

A: We have given that events P(A) =0.6 P(B) =0.5 P(A∪ B) = 0.8 Note: According to Bartleby expert…

Q: Let's say (B₁, B₂, B3, B4, B5) is a collection of events that are mutually exclusive events. If…

A: Two events are said to be mutually exclusive if both of them cannot occur at the same time. Two…

Q: A mouse is put inside a big room in which there are 4 exits through which the mouse can try to…

A: The traps at the exits, functions properly with probabilities, 0.3, 0.2, 0.3, and 0.5 respectively.…

Q: Suppose that A and B are two independent events for which P(A)=0.32 and P(B)=0.7. Find each of the…

Q: Let A and B be events. Assume that P(A) = 0.55, P(B|A) = 0.36, and P(B|A') = 0.84. Then, P(A∩B)=?,…

A: P(A) = 0.55P(B|A) = 0.36P(B|A') = 0.84

Q: A box is filled with several party favors. It contains 12 hats, 15 noisemakers, ten finger traps,…

A: The following information has been provided: Number of hats=12 Number of noisemakers=15 Number of…

Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…

Q: If event A and event B are mutually exclusive, and P(A) = 0.5 and P(B) = 0.3, find P(A and B).

A: From given data we have : P(A)=0.5 P(B)=0.3

Q: Photos and videos have become an important part of the online social experience, with more than half…

A: P(A) =0.52P(B) = 0.26P(A or B) = 0.54

Question

Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let

A₁

be the event that the receiver functions properly throughout the warranty period,

A₂

be the event that the speakers function properly throughout the warranty period, and

A₃

be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with

P(A₁) = 0.93,

P(A₂) = 0.92,

and

P(A₃) = 0.70.

(Round your answers to four decimal places.)

(a)

What is the probability that all three components function properly throughout the warranty period?

(b)

What is the probability that at least one component needs service during the warranty period?

(c)

What is the probability that all three components need service during the warranty period?

(d)

What is the probability that only the receiver needs service during the warranty period?

(e)

What is the probability that exactly one of the three components needs service during the warranty period?

Video Video

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 with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that A and B are two independent events for which P(A)=0.23 and P(B)=0.65. Find each of the following: A. P(A|B)= B. P(B|A)= C. P(AandB)= D. P(AorB)=
Show that the probability that an event A or an event B or both will occur is given by the formula P(AUB) = P(A)+P(B)– P(AnB), and specialise this formula for the case (a) when A, B are mutually exclusive events and for the case (b) where A, B are statistically independent events. Find the probabilities P(A), P(B) when A, B are statistically independent events such that P(B) = 2P(A) and P(AU B) = 5/8.
b. Determine P(F or D)= P(F or D). (Type an integer or a decimal.) c. Find the probability that a randomly selected adult is male. P(male) = (Type an integer or a decimal.)
Suppose that A, B and C are three independent events such that P(A)=0.2, P(B)=0.5 and P(C)=0.1. Determine the probabilty that none of these events occurs. Answer in procent.
Please answer d and e. P.9.2
Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.
Determine if events A and B are independent: P(A) = 0.3 P(B) = 0.6 P(A ∩ B) = 0.18
Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A₁ be the event that the receiver functions properly throughout the warranty period, A₂ be the event that the speakers function properly throughout the warranty period, and A3 be the event that the CD player functions properly throughout the warranty period. Suppose that these events are (mutually) independent with P(A₁) = 0.92, P(A₂) = 0.96, and P(A3) = 0.90. (Round your answers to four decimal places.) (a) What is the probability that all three components function properly throughout the warranty period? (b) What is the probability that at least one component needs service during the warranty period? (c) What is the probability that all three components need service during the warranty period? (d) What is the probability that only the receiver needs service during the warranty period? (e) What is the probability that exactly one of the three components needs service…
Suppose that in a large university, 40% of students work part time, 10% are part of one of the university's sports teams, and 5% both work part time and are part of one of the university's sports teams. Let W be the event that a student works part time, and V be the event that a student is part of one of the university's sports teams. Make sure all your answers are expressed in terms of the events W and V,. 4. А. What is the probability that a randomly selected student works part time or is a part of one of the university's sports teams? В. teams? What proportion of students do not work part time but are part of one of the university's sports С. Are W and V independent events? D. If a student works part time, what is the probability they are also part of one of the university's sports teams? Е. What proportion of students are not part of any of the university's sports teams and work part time?