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Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let A1 be the
(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?
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- If event A and event B are mutually exclusive, and P(A) = 0.5 and P(B) = 0.3, find P(A and B).arrow_forwardA commuter must pass through three traffic lights on her way to work. For each traffic light, the probability that it is green when she arrives is 0.6. The lights are independent. 3 (a) Compute the probability that all three lights are green. (b) The commuter goes to work five days per week. Let X be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. Determine the distribution of X. (c) Calculate P(X= 3).arrow_forwardSuppose 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)=arrow_forward
- Suppose that P(A) = 0.25 and P(B)= 0.4. If events A and B are mutually exclusive, find: P(ANB) а. b. Р(AUB)arrow_forwardLet 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.arrow_forwardConsider 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…arrow_forward
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
