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Probability Exam

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1—D
2A survey of 1000 people determines that 80% like walking and 60% like biking, and all like at least one of the two activities. What is the probability that a randomly chosen person in this survey likes biking but not walking? A) 0 B) .1 C) .2 D) .3 E) .4C
3(SOA) Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by .14 the probability that a patient visits a physical therapist. Determine the probability that a randomly chosen member of this group visits a physical therapist. A) .26 B) .38 C) .40 D) .48 E) .62D
4(SOA) An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn. A) 4 B) 20 C) 24 D) 44 E) 64A
5(SOA) An actuary is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of women. For each of the three factors, the probability is 0.1 that a woman in the population has only this risk factor (and no others). For any two of the three factors, the probability is 0.12 that she has exactly these two risk factors (but not the other). The probability that a woman has all three risk factors, given that she has A and B, is 1/3. What is the probability that a woman has none of the three risk factors, given that she does not have risk factor A? A) .280 B) .311 C) .467 D) .484 E) .700C
6A class contains 8 boys and 7 girls. The teacher selects 3 of the children at random and without replacement. Calculate the probability that number of boys selected exceeds the number of girls selected. A) 512/3375 B) 28/65 C) 8/15 D) 1856/3375 E) 36/65A
7A store has 80 modems in its inventory, 30 coming from Source A and the remainder from Source B. Of the modems from Source A, 20% are defective. Of the modems from Source B, 8% are defective. Calculate the probability that exactly two out of the random sample of five modems from the store’s inventory are defective. A) .010 B) .078 C) .102 D) .105 E) .125C
8Two life insurance policies, each with death benefit of 10,000 and a one-time premium of 500, are sold to a couple, one for each person. The policies will expire at the end of the tenth year. The probability that only the wife will survive at least ten years is .025, the probability that only the husband will survive at least ten years is .01, and the probability that both of them will survive at least ten years is .96. What is the expected excess of premiums over claims, given that the husband survives at least ten years? A) 350 B) 385 C) 397 D) 870 E) 897E
9A probability distribution of claim sizes for an auto insurance policy is given in the table below: Claim Size Probability 20 .15 30 .10 40 .05 50 .20 60 .10 70 .10 80 .30 What percentage of the claims are within one standard deviation of the mean claim size? A) 45% B) 55% C) 68% D) 85% E) 100%A
10A life insurer has created a special one year term insurance policy for a pair of business people who travel to high risk locations. The insurance policy pays nothing if neither dien in the year, $100,000 if exactly one of the two die, and $K>0 if both die. The insurer determines that there is a probability of .1 that at least one of the two will die during the year and a probability of .08 that exaclyl one of the two will die during the year. You are told that the standard deviation of the payout is $74,000. Find the expected payout for the year on this policy. A) 18,000 B) 21,000 C) 24,000 D) 27,000 E) 30,000A
11—A
12—A
13—C
14—E
15—E
16—E
17—A
18—D
19—D
20—C
21—C