Q1: If the event A is independent with itself, then P(A) is
Q: Let A and B be two events such that P(A|B)=P(A|BC), where BC is the complement of B), and 0 < P(B) <…
A: We use the conditional probability formula to prove that A and B are independent.…
Q: Assume A and B are independent events with P(4)=0.2 and P(B)-0.5. Let D be the event that exactly…
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Q: Let A, B be two mutually exclusive events such that AUB = 2, p(A) = 4p(B). Find p(B - A) Select one:…
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Q: Let C and D be events such that Pr[C] =0.8, Pr[D] =0.6,and Pr [C ∪ D] =0.9. Find.. Pr[C |…
A: Given, The objective is to find the required probabilities.
Q: Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math…
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Q: What is the probability that all three components function properly throughout the warranty period?…
A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted
Q: 4. Show that an event A is independent of itself iff P(A) is either 0 or 1.
A: Proof: PA=PA∩A=PAPA Since A is independent itself.⇒PA1-PA=0PA=1 Since P(A)>0
Q: let A and B be two events in an outcome space M such that M = A U B, P (A) = 0.65 and P (B) = 0.75.…
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Q: Supposed P(F) = .25, P(F or G) = .70, and events F and G are mutually exclusive. Find: a) P(G)…
A: (a)If events F and G are mutually exclusive, then, P (F or G) = P(F)+ P(G).Or, P(G) = P (F or G) –…
Q: Suppose that the events A, B, and C are independents, where P(A)= 1/2, P(B)=1/3, and P(C)= 1/4. What…
A: Given that A, B, and C are independents. So,…
Q: Which of the following statements is true of P(A), that is, the probability of A, for any event A?…
A: I. If A is very likely to occur, P(A) > 1 II. P(A) = 1 - P(A not occurring) III. P(A) > 0…
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: Show the technical theorem for the following: Suppose A1, A2, B are events such that P(A1 ∩ B) > 0.…
A: Probability is the chance that an unsure event will occur with this probability. Basically, the…
Q: Q1: If the event A is independent with itself, then P(A) is
A: The statement is the event A is independent itself.
Q: Let event C=taking an English class. Let event D=taking a mathematics class. Suppo P(C) =0.75,…
A: The question is about probability of events Given : C : Taking an English class D : Taking a…
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: (b) Apply Bayes theorem, PA, I8) KAJP0IA,)+PA,Pte |A,) RAO TA to compute the posterior (a) Compute…
A: Given, P(A1) = 0.2 P(A2) = 0.3 P(A3) = 0.5 P(B | A1) = 0.3 P(B | A2) = 0.4 P(B | A3) = 0.2
Q: Let A, B and D be events. Show that p(A ∪ B|D) = P(A|D) + P(B|D) − ?(A ∩ B|D).
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Q: Let A and B be events. Point (prove) that: a. P(A \ B) = P(A) − P(A ∩ B). b) If 0 < P(B) < ,…
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Q: Let A and B be events. Show that each of the following is true. (a) 1+ P(An B) ≥ P(A) + P(B) (b) P…
A: We have to prove the given statements for the probability of events A and B.
Q: Let A and B be events of positive probability. Prove that P(A|B) ≥ P(A) if and only if P(B|A) ≥…
A: A and B are events of positive probabilityi.e. P(A)>0 and P(B)>0Want to prove that P(A|B) ≥…
Q: Which of the following statements is true of P(A), that is, the probability of A, for any event A?…
A: Probability defination: Probability may be defined as the ratio of favourable outcome to total…
Q: 2. In a Mathematical Finance class, students can purchase shares of stock in Amazon, Tesla, and…
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Q: Let event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math…
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Q: 8. Let A, B and C be three events such that P(BOC) > 0. Prove or disprove each of the following…
A: a) P(An BC) = P(A|BC)P(BC) is actually true. This can be proven using the conditional probability…
Q: Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a…
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Q: Which statement(s) is(are) always true v[Select ] D. P(A) < 1 for any event A Neither C nor D Both C…
A: In question, We'll select the correct option. The explanation is below,
Q: 2. Let 0 0, P(B| A) = P(B|A), then that event A and B are independent. prove
A: We need to prove, P(AnB) = P(A)P(B)
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: If S and T are mutually exclusive events then P(S|T) is P(SnT) P(S) P(SnT) o P(T) 1 近
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Q: Let A and B be any two events defined on S. suppose that p(A)=0.2, p(B)=0.7, and p(A and B)=0.3, the…
A: It is given that, p(A) =0.2 p(B) =0.7 and p(A and B) =0.3
Q: If A and B are independent events, then ... None of the above OP(AUB)=P(A)×P(B) OP(A U B) = 1OP(An…
A: If events A and B are independent, it means that the occurrence or non-occurrence of one event does…
Q: If A and B are independent events. Then A and BC are independent.
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Q: Let A and B be events such that Pr[A] = 0.43, Pr[B] = 0.54, and Pr[A ∩ B] = 0.23. Find …
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Q: If A and B are independent events. Then AC and BC are also independent events.
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- . If A is an arbitrary event, then show that P(A) = 1- P(A).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.Let A and B be events such that 0 < P(A) < 1 and 0 < P(B) < 1. a. Show that if A and B are independent, then P(AN B) # 0. b. Show that if P(AN B) = 0, then A and B are not independent
- Let B₁..... B, be independent events. Show P(UB)=1-1-PC P(B₁)). imlProve the theoremLet event G = taking a math class. Let event H = taking a science class. Then, G ∩ H = taking a math class and a science class while G ∪ H = taking either a math class or a science class. Suppose P(G) = 0.42, P(H) = 0.45, and P(G ∪ H) = 0.25. What is P(G ∩ H)
- 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…a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery 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?
- A sample of 20 products are selected from output of a production line which contains 6 defective products.Let A be the event that the first product drawn is defective, and let B be the event that the second product drawn isdefective.Find P(A)Find P(B|A)Find P(A ∩ B)Find P(Ac ∩ B)Find P(A|B)Show that for any events A and B, P (A ∩ B) ∪ (A ∩ B) = P(A) + P(B) − 2P(A ∩ B)
