[开课学院]: 资电学院(ex:金融学院,商学院,理工学院,资电学院,建设学院,文学院...) [开课系所]: 资讯系(ex:中文系,外文系,电机系,财税系..) [课程名称]: 机率论 [老师名称]: 游景盛 老师 [开课学期]: 972 [类型]: 第一章小考ex:(第n次)小考/98-2期中考/98-2期末考 1. Define a sample space for the experiment of putting three different books on a shelf in random order. If two of these three books are two-volume dictionary,describe the event that these volumes stand in increasing order side-by-side (i.e. volume Ⅰ precedes volume Ⅱ). 2. A limousine that carries passengers from an airport to three different hotels just left the airport with two passengers. Describe the sample space of the stops and the event that both of the passengers get off at the same hotel. 3. Suppose that 35% of the people have O+ blood and 6% have O-. What is the probability that the next president of the United States has type O blood? P(A)=P(AB)+P(AB')=35+6=41% 4. Suppose that the probability that a driver is a male, and has at least one motor vehicles accident during a one-year period, is 0.12. Suppose that the corresponding probability for a female is 0.06. What is the probability of a randomly selected driver having at least one accident during the next 12 months? 5. A card is drawn at random from an ordinary deck 52 cards. What is the probability that it is (a)a black ace or a red queen;(b)a face or a black card;(c)neither a heart nor a queen? (a)2/52+2/52=4/52 (b)12/52+26/52-6/52=32/52 (c)1-(13/52+4/52-1/52)=32/52 6. A ball is thrown at a square that is divided into n^2 identical squares. The probability that the ball hits the square of the ith column and jth row n n is Pij, where Σ Σ Pij=1. In terms of Pij's, find the probability that i=1 j=1 the ball hits the jth horizontal strip. 7. Two numbers are successively selected at random and with replacement from the set {1,2,…,100}. What is the probability that the first one is greater than the second? 8. A bus arrives at a station every day at a random time between 1:00P.M. and 1:40P.M. What is the probability that a person arriving at this station at 1:00P.M. will have to wait at least 30 minutes? 9. A number is selected at random from the set of nutural numbers {1,2,…,1000}. What is the probability that it is not divisible by 4,7,or 9? 10.A number is selected at random from the set {1,2,3,…,150}. What is the probability that it is relatively prime to 150? 11.From a small town 120 persons were selected at random and asked the following question: Which of the three shampoos,A,B,or C,do you use? The following results were obtained:20 use A and C,10 use A and B but not C, 15 use all three,30 use only C,35 use B but not C,25 use B and C, and 10 use none of three. If a person is selected at random from this group. What is the probability that he or she uses(a)only A;(b)only B;(c)A and B? (Draw a Venn diagram.) --

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