HW2Solution - Geostatistics Petroleum and Geosystems...

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Geostatistics Petroleum and Geosystems Engineering 337 (19065) Spring 2008 Homework Assignment #2 Section 2.1 (Page 60) 3. A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four answers are recorded. a List all 16 outcomes in the sample space. Ans According to the given, we can select either true or false 4 times for one completed answer. TTTT, TTTF, TTFT, TFTT FTTT, FFTT, FTFT, FTTF, TFFT, TFTF, TTFF, TFFF, FFFT, FFTF, FTFF, FFFF b Assuming the outcomes to be equally likely, find the probability that all the answers are the same. Ans From the list of 16 outcomes, there are only 2 outcomes giving the same answers (TTTT, FFFF). Hence, the probability is 2/16 or 1/8 c Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is “True”. Ans From the list of 16 outcomes, there are only 4 outcomes having one “True” in the answer. Hence, the probability would be 4/16 or 1/4 d Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is “True”. Ans This is an extension of part c; we know from part c that the probability of exactly 1 “True” is 4/16. But the question asks “at most” 1 “True” which means we need to include the case of 0 “True” which is the FFFF outcome, which makes the answer to this question 5/16 .
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5. A box contains four bolts. Two of them, labeled #1 and #2 are 5 mm in diameter, and two of them, labeled #3 and #4 are 7 mm in diameter. Bolts are randomly selected until a 5 mm bolt is obtained. The outcomes are the sequences of bolts that can be selected. So one outcome is 1, and another is 342. a List all possible outcomes. Ans For all outcomes, we can randomly selected four of them until we’ve got either 1 or 2 since both have 5 mm diameter. Hence, there will be 10 outcomes in total as shown below. 1, 2, 31, 32, 341, 342, 41, 42, 431, 432. b Let A be the event that only one bolt is selected, list the outcomes in A. Ans A - ( 1, 2) c Let B the event that three bolts are selected. List the outcomes in B. Ans B - (341, 342, 431, 432) d Let C be the event that bolt#2 is selected. List the outcomes in C. Ans C - (2, 32, 342, 42, 432) e Let D be the event that bolt#4 is NOT selected. List the outcomes in D.
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HW2Solution - Geostatistics Petroleum and Geosystems...

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