無年度 - 主題課程_商學院統計：古典機率#107840

試卷資訊

選擇題 (4)

Let A and B be the events such that = 0.4, = 0.6, and . Then =?, =?(A) (B) (C) (D) (E)以上皆非

Suppose that A, B and C are three independent events such that = 0.6, = 0.4, = 0.2. What is the probability that exactly one of these three events will occur? (A)0.371 (B)0.398 (C)0.407 (D)0.464

Given the probabilities of somc of events as follows: P(C|B) =0.95, =0.3, = 0.2, = 0.05, = 0.35,= 0.2.Compute P(AIB). (A)0.2021 (B) 0.2075 (C)0.2098 (D) 0.2132

A Bayesian approach can be used to revise probabilities that a prospect field will produce oil. In one case, geologica! assessment indicates a 25% chance that the field will produce oil. Further, there is an 80% chance that particular well will strike oil given that oil is present in the prospect filed. Suppose that one well is drilled on the field and it comes up dry. What is the probability that the prospect filed will produce oi?? (A)0.0333 (B)0.0425 (C)0.0625 (D)0.0675

申論題 (3)

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10% by rural areas. Of the municipal bonds rated B, 60% were issued by cities, 20% by suburbs, and 20% by rural arcas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs, and 5% by rural areas. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating?

Q1.(10%) Consider two events A and B, prove that if A and B are independent, then so are .

Three events: A₁, A₂ and B are given. We know that A₁ and A₂ are disjointed events. P(A₁)>0 and P(A₂)>0. Let P(B|A₁)= P(B|A₂)=0.2. Please find P(B|A₁UA₂).