Exam1_06

# Exam1_06 - CEE 304 Uncertainty Analysis in Engineering...

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CEE 304 – Uncertainty Analysis in Engineering Prelim 1- October 4, 2006 SHOW WORK. You may use the text, your notes, and calculators. There are 50 points in total. You have 50 minutes. 1. (8 pts) There are four events of interest, A, B, C and D. You know that P(A) = 0.2, P(B) = 0.3, P(C) = 0.4, P(D) = 0.5; and P(A|B) = 0.8, P(B C) = 0.6. (a) In the long run, what is the probability that both event A and event B occur? (b) What is the probability that both B and C occur? (c) If B is known to have occurred, what is the probability that C occurs? (d) If B and D are independent, what is the probability that at least one of B or D occurs? 2. (13 pts) A pharmaceutical firm obtains a reagent from two different sources: Enriched Inc. and Low_Go. The reagent should have a concentration of 12 mg/l, but there is variation, which is acceptable. 70% of the reagent from Enriched has a concentration greater than 12 mg/l, whereas Low_Go provides a reagent with a concentration greater than 12 mg/l only 20% of the time. Assume that 90% of the reagent comes from Enriched, and 10% from Low_Go. Solutions are NOT mixed. (a) What is the probably a randomly sample will have a concentration greater than 12 mg/l? (b) If I obtained a sample with a concentration greater than 12 mg/l, what is the probability it was supplied by Enriched, Inc? (c) If I started examining samples that have been collected randomly in the past, what is the mean and variance of the number of samples I will examine before I pick one from Low_Go? (d)

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## This note was uploaded on 02/02/2008 for the course CEE 3040 taught by Professor Stedinger during the Fall '08 term at Cornell.

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Exam1_06 - CEE 304 Uncertainty Analysis in Engineering...

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