单选题 An insurance company estimates that 40% of policyholders who have only an auto policy willrenew next year, and 60% of policyholders who have only a homeowner policy will renew next year. The company estimates that 80% of policyholders who have both an auto and ahomeowner policy will renew at least one of those policies next year. Company records showthat 65% of policyholders have an auto policy, 50% of policyholders have a homeowner policy,and 15% of policyholders have both an auto and a homeowner policy. Using the company'sestimates, what is the percentage of policyholders that will renew at least one policy nextyear?

单选题 The law of total probability is an important application of conditional probability, which statesthat the total probability of an event can be reconstructed using conditional probabilitiesunder the condition that the probability of the sets being conditioned is equal to 1. Which of the following statements is a correct application of the total probability theorem?

单选题 Let f(x) represent a probability function (which is called a probability mass function, p.m.f., fordiscrete random variables and a probability density function, p.d.f., for continuous variables)and let F(x) represent the corresponding cumulative distribution function (CDF); in the caseof the continuous variable, F(X) is the integral (aka, anti-derivative) of the pdf. Each of thefollowing is true about these probability functions EXCEPT which is false?

单选题 For a certain operational process, the frequency of major loss events during a one period yearvaries form zero to 5.0 and is characterized by the following discrete probability mass function (pmf) which is the exhaustive probability distribution and where (b) is a constantLoss event (X) 0 1 2 3 4 5PMF(f(x)) 12b 7b 5b 3b 2b 1bWhich is nearest to the probability that next year LESS THAN two major loss events willhappen?

单选题 An analyst is examining a portfolio that consists of 1,000 subprime mortgages and 600 primemortgages. Of the subprime mortgages, 200 are late on their payments. Of the primemortgages, 48 are late on their payments. If the analyst randomly selects a mortgage fromthe portfolio and it is currently late on its payments, what is the probability that it is asubprime mortgage?

单选题 In country X, the probability that a letter sent through the postal system reaches itsdestination is 2/3. Assume that each postal delivery is independent of every other postaldelivery, and assume that if a wife receives a letter from her husband, she will certainly maila response to her husband. Suppose a man in country X mails a letter to his wife (also incountry X) through the postal system. If the man does not receive a response letter from hiswife, what is the probability that his wife received his letter?

单选题 Suppose there are two events A and B. The probability of A occurrence equals that of B. P(AB)= 4%, If event A occurred, the probability of B occurs is 80%. What is the probability of neitheroccurs?

单选题 Assume the probability density function (pdf) of a zero-coupon bond with a notional value of$$10.00 is given by 𝐟𝐟(𝐱𝐱) = 𝐱𝐱/𝟖𝟖 − 𝟎𝟎.𝟕𝟕𝟕𝟕 on the domain [6,10] where x is the price of thebond:𝑥𝑥f(x) = −0.75 s.t 6 ≤ x ≤ 10 where x = bond price8What is the probability that the price of the bond is between $$8.00 and $9.00?

单选题 An analyst develops the following probability distribution about the state of the economy andthe market.Initial Probability P(A) Conditional Probability P(B丨A)Bull market 50%Good economy 60% Normal market 30%Bear market 20%Bull market 20%Poor economy 40% Normal market 30%Bear market 50%Which of the following statements about this probability distribution is least likelyaccurate?