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math319_S10_Quiz3

# math319_S10_Quiz3 - in the factory M1 produces 35 M2...

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Math 319, Spring 2010 Quiz 3 Thursday, April 15, 2010 9.05-9.40 am Name : No use of notes or textbook - For full credit, show your work - Work alone 1. State the most general version of Bayes’ Formula, carefully introducing any terms you use. 1

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2. (a) Complete the following definition. Two events E and F are independent if (b) Consider the following events in the toss of a single die. A : an odd number is rolled. B : an even number is rolled. C : a 1 or 2 is rolled. (i) Are A and B independent events? Justify your answer using the definition in (a). (ii) Are A and C independent events? Justify your answer using the definition in (a). 2
3. (a) In a local factory, machines M1, M2, M3 are all producing springs of the same length. The machines M1, M2, M3 produce 2%, 1%, and 3% defective springs, respectively. Of the total production of springs
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Unformatted text preview: in the factory, M1 produces 35%, M2 produces 25%, and M3 produces 40%. One spring is selected at random from all the springs produced in a given day. If the selected spring is defective, what is the probability that it was produced by M3? Explain any terms you introduce in your answer. (b) You know that a certain letter is equally likely to be in any one of three diﬀerent folders. Let α i (which may be < 1) be the probability that you will ﬁnd your letter upon making a quick examination of folder i , if the letter is, in fact, in folder i , i = 1 , 2 , 3. Suppose you look in folder 1 and do not ﬁnd the letter. What is the probability that the letter is in folder 1? Explain any terms you introduce in your answer....
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math319_S10_Quiz3 - in the factory M1 produces 35 M2...

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