15 September 2014 MKMI 2893/MMN 2353 Assignment 1 – Introduction to Probability Review Answer all questions and please show your work clearly. 1. Describe a random or uncertain phenomenon that you have dealt with either at work or in life. 2. Give 3 samples or observations of a “random” phenomenon. Be creative if you like. Describe the “random experiment” and the “sample space”. 3. LCD televisions are given a final inspection following assembly. The three types of defects are identified as critical, major, and minor defects and are coded A, B, and C, respectively. Data are analyzed with following results, Sets having only critical defects 3% Sets having only major defects 2% Sets having only minor defects 10% Sets having only critical and major defects 4% Sets having only critical and minor defects 5% Sets having only major and minor defects 3% Sets having all three types of defects 1% a. What fraction of the sets has no defects? b. Sets with either critical defects or major defects (or both) get a complete rework. What fraction falls under this category? 4. A single bolt is selected at random from a box of 10,000. Three different kinds of defects, A, B, and C, are known to occur in these particular bolts. Type A defects occur 1 percent of the time, type B defects occur 0.5 percent of the time, and type C occur 0.75 percent. In addition, it is estimated that 0.25 percent have both A and B defects, 0.30 percent have both A and C, 0.20 percent have B and C, and 0.10 percent have all three defects. What is the probability that the sample bolt has at least one of the three types of defects? 5. Consider an experiment to determine the speed of a molecule of a particular gas. Is this a deterministic or nondeterministic experiment? Why? If the experiment is nondeterministic describe the sample space. 6. Three printing companies do work for the publications office of UTM Press. The publications office does not negotiate a contract penalty for late work, and the data below reflect a large amount of experience with these companies. Company Fraction of contract held by company 1 2 3 0.2 0.3 0.5 Fraction of time delivery more than one month late 0.1 0.4 0.2 A department observes that its booklet is more than one month late, what is the probability that the contract is held by printing company 3? Page 1 of 2 7. Consider the diagram of an electronic system, which shows the probabilities of the system components operating properly. What is the probability that the entire system operates if assembly III and at least one of the components in assembly I and II must operate for the assembly to operate? Assume that the components of each assembly operate independently and that the assemblies operate independently. 8. By accident, a chemist combined two laboratory substances that yielded a desirable product. Unfortunately, her assistant did not record the names of the ingredients. There are forty substances available in the lab. If the two in question must be located by successive trialand-error experiments, what is the maximum number of tests that might be made? Due date is 22 September 2014 at the beginning of lecture. If there are any questions or any clarifications on this assignment, please email me at [email protected]. Late homework will NOT be accepted. Page 2 of 2