midterm1 - Math 3101 Midterm I October 19, 2010...

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Unformatted text preview: Math 3101 Midterm I October 19, 2010 Instructions: Do all work and record all answers in the blue book, affixing your name and instructor’s name on front cover. Whenever possible indicate the sample space Q and its cardinality Answers 52) may be left in that form need not be simplified beyond finite sums and products; for example ( 5 whereas 2;”:2 3'” should be simplified. Each problem counts 20 points. 1. A child has five identical red blocks, four identical green blocks, and one yellow block. Suppose the child stacks these ten blocks randomly on top of one another (a) In how many distinguishable ways can this be done? (b) Compute the probability that blocks of like color end up stacked together (i.e., the 5 red blocks are stacked consecutively and the 4 green blocks are stacked consecutively)? 2. (a) In a twenty—question true—false exam, find the probability that a. student gets at least 70 percent correct by guessing. (b) Given that a student gets 7'0 percent correct, what is the probability that the student gets at least 90 percent? 3. The members of a consulting firm rent cars from 3 rental companies: 60 percent from Company A, 30 percent from Company B, and 10 percent from Company C. The past statistics show that 9 percent of the cars from Company A need a tune—up, 20 percent of the cars from Company B need a tune-up, and 6 percent of the cars from Company C need a tune-up. If a rental car delivered to the firm needs a tune-up, what is the probability that it came from Company B? 4. A group of 5 people are interviewed in order to determine the month in which they were born. Assume for simplicity that all months are equally probable. Compute the probabilities of the following events: (a) All 5 people have different birth-months. (b) One pair of peOple has the same birth—month, a second pair of people has the same birth month (but a different month from the first pair), and the fifth person has a different birth month from the rest of the group. 5. Consider a succession of rolls of a fair die. (a) Define the random variable X to be the number of rolls at which 6 appears for the first time. i. Compute P(X = 4). ii. Compute P(X even). iii. Compute P(X > 5[X even). (b) Define the random variable Y to be the number of rolls at which 6 appears for the 4th time. Compute PG” = 20). ca ,_{2_= 52,490 é}, fosscfia gtsLAVAt-XW . S . @) (afar: am 31244 Jafaflfly) : ._ Jig/4! 6149/ W! [o] 29 “a: 0:26 ZO"Jche/& 91% alt/Veg. 641/616,” .—-—-— / W7: (9 /? Jormo-J/ 4917324) I 20 Z 20 0 ffifi) {fats $21” Z -& a) $514 7963)? 0 3 ?(T/@)= a; TKCVO’ Tfi/c) 0.0g KFCE/‘fl = Z nr— 0‘ ‘ ‘ ’PCT) 0.09% M20“ 0060.: 0‘06 _ otaé FL 0,054+0L0é-1k0i00g _ 0J2. ‘— Z. ,_._._ .u. ...
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midterm1 - Math 3101 Midterm I October 19, 2010...

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