Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Probability and Statistics EQT 272 Semester 1 2016/2017 TUTORIAL 1 1) A random car is chosen among all those passing through The Store on a certain day. The probability that the car is red is 0.4, the probability that the driver is a student is 0.3 and the probability that the car is red and the driver is a student is 0.05. A car is selected at random, calculate the probability that (i) the car is red or belongs to a student ans: 0.65 (ii) the car is not red and does not belongs to a student ans: 0.35 2) The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4 and 0.2, respectively. Let A denote the event {a, b, c} and let B denote the event {c, d, e}. Determine the following: (i) P( A) ans: 0.4 (ii) P(B) ans: 0.8 (iii)P( Aï‚¢) ans: 0.6 (iv) P( A  B) ans: 1 (v) P( A  B) ans: 0.2 3) Suppose we randomly select two persons from the members of a club and observe whether the person selected each time is a man or a woman. Write all the outcomes for this experiment. Draw the tree diagrams. 4) A candy dish contains one yellow and two red candies. You close your eyes, choose two candies one at a time from the dish, and record their colours. What is the probability that both candies are red? ans: 1/3 5) A printed circuit board may be purchased from seven suppliers. In how many ways can three suppliers be chosen from the seven? ans: 35 ways 6) There are 5 yellow balls, 4 red balls and 3 blue balls in a box. In how many ways can a child choose 4 balls from the box without any particular order? What is the probability that the child choose 2 yellow balls, 1 red ball and 1 blue ball? ans: 495 ways, 0.2424 Probability and Statistics EQT 272 Semester 1 2016/2017 7) Suppose 20 students share the same floor of a dormitory. 11 of them took Statistics class, 8 took Chemistry class and 3 took both Statistics and Chemistry classes. A student is chosen at random from 20 students. What is the probability he took either the Statistics or Chemistry classes? What is the probability he did not take any of the two classes? ans: 0.8, 0.2 8) Consider the following events for an experiment of rolling a fair dice. A= an even number is observed B= an odd number is observed C= a number less than 4 is observed Are events A and B mutually exclusive? Are events B and C mutually exclusive? Draw a venn diagram for events A, B and C. ans: A and B are mutually exclusive, B and C are not mutually exclusive 9) How many four-letter code words are possible using the letters in TYPE if (i) the letters may be repeated? ans: 256 (ii) the letters may not be repeated? ans: 24 10) Toss two coins and observe the outcome. Define these events and its probability: A: head on the first coin B: tail on the second coin Are events A and B independent? ans: A and B are independent 11) 30% of all computer used by government agencies are supplied by company A and the rest by company B. 5% of all computers supplied by company A are defective while 2% of all computers supplied by company B are defective. (i) How many percent of all computers used are defective? ans: 2.9% (ii) A computer is found to be defective. What is the probability it was supplied by company B? ans: 0.4828 12) A statistics class for engineers consists of 25 industrial, 10 mechanical, 10electricaland 8 civil engineering students. If a person is randomly selected by theinstructor to answer a question, find the probability that the student chosen is (i) an industrial engineering major. ans: 25/23 (ii) a civil engineering or an electrical engineering major. ans: 18/53 Probability and Statistics EQT 272 Semester 1 2016/2017 13) John is going to graduate from an industrial engineering department in a university by the end of the semester. After being interviewed at two companies he likes, he assesses that his probability of getting an offer from company A is 0.8, and the probability that he gets an offer from company B is 0.6. If on the other hand, he believes that the probability that he will get offers from both companies is 0.5, what is the probability that he will get at least one offer from these two companies? ans: 0.9 14) Suppose the manufacturer specifications of the length of a certain type of computer cable are 2000 ± 10 millimeters. In this industry, it is known that small cable is just as likely to be defective (not meeting specifications) as large cable. That is, the probability of randomly producing a cable with length exceeding 2010 millimeters is equal to the probability of producing a cable with length smaller than 1990 millimeters. The probability that the production procedure meets specifications is known to be 0.99. (i) What is the probability that a cable selected randomly is too large? ans: 0.005 (ii) What is the probability that a randomly selected cable is larger than 1990 millimeters? ans: 0.995