a) Prove the De Morgan's rule for events A and B using Venn diagram
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A: Given: Event A= getting atleast one defective calculator when 4 are randomly selected Then to write…
Q: Suppose that A and B are mutually exclusive events. a. Use the special addition rule to express P(A…
A: a. Events A and B are mutually exclusive. Special addition rule is used. Special Addition Rule If…
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A: here use given contingency table
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A: If the knowledge that an event A has occurred implies that a second event B cannot occur, then the…
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A: It is given that P(A) = 8/21 P(B) = 12/21 P(A or B) = 17/21
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A: Answer : Given: General manager = 1 Marketing Director = 1 Employees of company A = 3 Vice president…
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A: Here use binomial theorem
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A: P(A) = (70 + 16) / 100 = 86 / 100 = 0.86 P(B) = (70 + 9) / 100 = 79 / 100 = 0.79 P(AB) = Probability…
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A: As per our guidelines, we are allowed to answer first three sub-parts only. Thanks Given :
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Q: Theorem 3-9. If A, B, C are mutually independent events then A UB and C are also ndependent.
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A: As per our guidelines we can solve first multiple-choice question and rest can be reposted.…
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Q: An experiment is a * O Collection of events.
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A: It is given that a manufacturer obtains clock-radios from three different subcontractors are 40%…
Q: 4. It is an event that has no connection to another event's chances of happening (or not happening).…
A: Here we have to identify the correct option as per given statement
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Q: 1. Suppose that the events A, B are independent. (a) Using the Law of Total Probability, show that…
A: Result: If A and B are independent then P(A and B)=P(A)P(B)
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A: S={HH,HT,TH,TT} A={HH} B={TT}
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A: An experiment consists of picking one of two urns at random and then selecting a ball from the urn…
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A: Mutually Exclusive Events: If the events E and F are mutually exclusive events, then there is no…
Q: Suppose that 30% of RunningWithTheDevil’s female visitors previously visited LetsRun.com and 10% of…
A: Probability that a customer is a female is: PFemale=12=0.5 Probability that a customer is a male is:…
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- For a parrallel structure of identical components the system can succeed if one of the component succeeds. Assume that the components fail independently of each other and that each component has a 0.11 probability of failure. a.) would it be unusual to observe one component fail? it ____ be unusual to observe one component fail since the probability that the component fails, ___ is ___ than 0.05. It ___ be unusual to observe two components fail since the probability that two components fail __ is __ than 0.05 b.) what is the probability that a parrallel structure with 2 identical components will succeed? c.) how many components would be needed in the structure so that the probability the system will succeed is greater than 0.9999?Consider a biased random walk on the set { 1, 2, 3, 4} withprobability p = .2 of moving to the left. What is the probability of moving from 2 to 3 in exactly 3 steps if the walk hasa. reflecting boundaries? b. absorbing boundaries?What is the simple random walk on integers? Does it always return to the origin if p = ½ ? if p ≠ ½?
- 1. Find the probability that the circuit operates. 2. It is known that the circuit is operating, find the probability that device A is functional.In the system in Figure 2.7, each component fails with probability 0.3 independently ofother components. Compute the system’s reliability.Anuja is at the bottom left (0, 0) of a coordinate grid of size n ∗ m, and she can only move right and up unit distance along the edges (She cannot move towards the right and above of the point (n, m)). She chooses a path randomly and every path is equally likely. What is the probability that she passes through a point (x, y) in her path? (x>=0 and x<=n and y>=0 and y<=m)
- A plane is missing and is presumed to have equal probability of going down in any of three regions. If a plane is actually down in region i, let 1 − αi denote the probability that the plane will be found upon a search of the ith region, i = 1, 2, 3. What is the conditional probability that the plane is in a region 1, given that the search of region 1 was unsuccessful? b region 2, given that the search of region 1 was unsuccessful? c region 3, given that the search of region 1 was unsuccessful?6. A smoke detector system uses two devices, an ionization sensor and a photoelectric sensor. If smoke is present, the probability that it will be detected by the ionization sensor (I) is 0.90, by the photoelectric sensor (P), 0.80, and by both devices, 0.72. a) Draw a Venn diagram to represent the problem. b) If smoke is present, determine the probability that the smoke will be detected by the system. c) if smoke is present, determine the probability that the smoke is undetected. d) are the two alarms operating independently. Justify your answer with a calculation.what is the step by step basis taken to solve the following jump discontinuity?
- This problem demonstrates the concept of redundancy, the principle of improving reliability of systems by using redundant or backup components. Suppose a hydraulic system on an airplane has a 5% probability of failing. a) What is the probability that the hydraulic system does not fail (that is, the flight is completed safely)? b) Now, suppose that the airplane has three independent hydraulic systems that each have a 5% probability of failure. What is the probability that all three systems fail? c) Supposing that the airplane will safely complete its flight if at least one of the three independent hydraulic systems is functioning, what is the probability that the airplane will safely complete its flight? d) What effect does having a redundancy of three independent hydraulic systems have on the probability of a safe flight?(Please answer 2nd question ) 1. Assume that there are two types of driver: One is careful and has a 0.1% of being in an accident. The other type is careless and has a 1% chance of being in an accident. Assume that each type represents 50% of the population. If there is a law mandating that all drivers buy insurance that would cover $100,000 in damages, the actuarially far premium for all drivers would be ________ while if there were no such law, the fair premium would be __________. Group of answer choices A) $100, $1,000 B) $100, somewhere between $100 and $1,000 C) $550, somewhere between $550 and $1,000 D) $550, 1,000 Ans :- option c ). 2. The term(s) used to describe the problem(s) that make the actuarially fair premiums different in the two cases in the question above is(are) Group of answer choices A) Asymmetric information B) Moral hazard C) Adverse selection D) A, B, and C E) A and CA hexagonal cell within a seven-cell system has a radius of 1.425 km. A total of 119 channels are used within the entire system. If the load per user is 0.028 Erlangs, and λ = 1 call/hour, compute the following for an Erlang C system (chart is attached) that has a 7% probability of delayed call: B) What is the probability that a delayed call will have to wait for more than 9 sec?
