math319_S10_Quiz1

# Math319_S10_Quiz1 - P E P F-2 P EF 3 A certain product was found to have two types of minor defect The probability that an item of the product has

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Math319, Spring 2010 Quiz 1 Thursday, February 18, 2010 9.05 - 9.45am Name : No use of notes or textbook - Show your work - Work alone 1. Consider an experiment whose sample space is S . For each event E of the sample space S , we assume that a number P ( E ) is deﬁned and satisﬁes three axioms. State these three axioms.

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2. Consider an experiment whose sample space is S and let E,F S be any events. Using the axioms you stated in Question 1 and consequences of these axioms that we proved in class, prove the following. (For full credit, explain your answer and justify each step.) (a) P ( EF c ) = P ( E ) - P ( EF ) . (b) The probability that exactly one of the events E or F occurs is given by
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Unformatted text preview: P ( E ) + P ( F )-2 P ( EF ) . 3. A certain product was found to have two types of minor defect. The probability that an item of the product has a type 1 defect is 0.2, and the probability that it has a type 2 defect is 0.3. Also, the probability that it has both defects is 0.1. Find the probabilities of the following events. (a) A is the event that an item has either type 1 defect or type 2 defect. (b) B is the event that an item does not have either of the defects. (c) C is the event that an item has defect 1 but not defect 2. (d) D is the event that an item has exactly one of the two defects....
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## This note was uploaded on 10/14/2010 for the course MATH 319 taught by Professor Clionagolden during the Spring '10 term at Bard College.

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Math319_S10_Quiz1 - P E P F-2 P EF 3 A certain product was found to have two types of minor defect The probability that an item of the product has

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