Homework 3 Solution (1)

# Homework 3 Solution - 1 ,Fall2011 Homework3(BasicsofProbability Due:ThursdaySeptember15 Name:SOLUTIONS Q.1 Consider two events P and Q a Write the

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CE 398 Introduction to Civil Engineering Systems Design, Fall 2011 Homework 3 (Basics of Probability for CE Systems Development) Due: Thursday September 15 Name: SOLUTIONS Q.1 Consider two events P and Q . a) Write the general formula used to calculate the probability that either event P occurs or Q occurs or both occur. p (P U Q) = p (P) + p (Q) – p (P ∩ Q) b) How does this formula change if … (i) Events P and Q are disjoint (that is, mutually exclusive of each other) (Give an example of such pair of events in everyday life or civil engineering) p (P U Q) = p (P) + p (Q) Example: Joe gets a final grade of A in CE398 Joe gets a final grade of B in CE 398 (ii Events P and Q are non-disjoint events that are statistically independent of each other. (Give an example of such pair of events in everyday life or civil engineering) p (P U Q) = p (P) + p (Q) – p (P)* p (Q) There is a recent serious earthquake in Lafayette This year’s winter is unusually severe (iii) Events P and Q are non-disjoint events that are statistically dependent of each other. (Give an example of such pair of events in everyday life or civil engineering) p (P U Q) = p (P) + p (Q) – p (P)* p (Q/P) or p (P U Q) = p (P) + p (Q) – p (Q)* p (P/Q) There is a serious earthquake in Lafayette Bridge systems in Lafayette suffer some deterioration 1

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Q.2. The probability that Joe is late for work is 0.20. The probability that Joe drives fast to work is 0.40. The probability that Joe does a good job at work is 0.75. Choose 3 letters, say L, D, G, to denote each of these events. If Joe is late, he the probability that he drives fast to work is 0.9. Also, assume that his punctuality (or otherwise) to work does not influence whether he does a good job that day. Furthermore, 30 out of every 100 days, he drives fast to work and does a good job in the same day. (a) For all paired combinations of these two events, comment on their mutual exclusivity, statistical dependence, or statistical independence. Use the table below.
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## This note was uploaded on 01/20/2012 for the course CIVIL ENGI 398 taught by Professor Labi during the Spring '11 term at Purdue University-West Lafayette.

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Homework 3 Solution - 1 ,Fall2011 Homework3(BasicsofProbability Due:ThursdaySeptember15 Name:SOLUTIONS Q.1 Consider two events P and Q a Write the

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