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# Probability MATH 351

Mason

GPA 3.85

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This 3 page Class Notes was uploaded by Michale Kuhlman on Monday September 28, 2015. The Class Notes belongs to MATH 351 at George Mason University taught by Harbir Lamba in Fall. Since its upload, it has received 65 views. For similar materials see /class/215004/math-351-george-mason-university in Mathematics (M) at George Mason University.

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Date Created: 09/28/15

H F a to Final Exam Answers Math 351 July 287 2005 Lim lf 5 cards are randomly selected from the standard 52 card deck7 what is the probability that they are all of the same suit 51482598960 How many ways can 4 boys and 6 girls be lined up7 if the boys must 7 CD a 0 USE d I D 1 3 120960 How many ways can 16 men be diVided into three groups of respective Q N a o a 1 3 7 960960 How many integer solutions does the following inequality have 1234 45 How many ways can a group of 3 students be chosen from a class of 40 students to work on a project 9880 How many 4 letter English words are possible if all letters must be different OJ 0 00 00 O Q How many 5 card poker hands are void in at least one suit 1913496 An urn contains 4 white balls and 9 black balls A ball is drawn at random What is the probability that it is white 413 An urn contains 4 white balls and 9 black balls Three balls are drawn one by one without replacement What is the probability that the third ball is white 4 13 H H H H to H OJ H a H T H 00 Two fair dice are rolled Given that the sum of the scores is greater than or equal to 87 what is the probability at least one die lands on 4 13 Suppose that 6 percent of men and 05 percent of women are colorblind A colorblind person is chosen at random What is the probability of this person being female Assume that there are an equal number of males and females Suppose that each child born to a couple is equally likely to be a boy or a girl independent of the sex distribution of the other children in the family For a couple having 4 children7 what is the probability that all children are of the same sex 1 8 The probability that A hits the target is 15 and the probability that B hits the target is 13 If they both shoot at the target7 what is the probability that at least one of them hit the target 1 H U A sample of 3 items is selected at random from a box containing 10 items of which 4 are defective Find the expected number of defective items in the sample If X is a random variable with EX 2VarX 037 nd the continued Find the variance of 2X 1 3 E12 If you roll a die until you get a 6 What is the probability that you have to roll at least six times 31257776 The probability of being dealt a full house in a hand of poker is approx imately 00014 Use Poisson distribution to approximate the probabil ity that in 1000 hands of poker you will be dealt at least 2 full houses m If you ip a fair coin 6 times what is the probability that head appears exactly 3 times 516 You arrive at a bus stop at 10 o clock knowing that the bus will arrive at some time uniformly distributed between 10 and 1030 What is the probability that you will have to wait longer than 15 minutes 2 H continued If at 1015 the bus has not yet arrived what is the prob 93 bility that you will have to wait at least an additional 10 minutes 13 If X is a normal random variable with parameters 1 10 and 02 36 If 65 percent of the population of a large community is in favor of a proposed rise in school taxes approximate the probability that a random sample of 100 people will contain between 60 and 70 inclusive who are in favor If X is uniformly distributed over 71 1 nd the density function of the random variable Y X2 All functions given below are 0 outside of the interval 01 1 m A television store owner gures that 38 percent of the customers en tering his store will purchase an ordinary television set 18 percent will percent will purchase a plasma television set and 44 percent will just be browsing lf 7 customers enter his store on a given day what is the probability that he will sell exactly 2 ordinary sets and 1 plasma set on that day A man and a woman agree to meet at a certain location about 1230 pm If the man arrives at a time uniformly distributed between 1215 and 1245 and if the woman independently arrives at a time uniformly distributed between 1200 and 1 pm nd the probability that the rst

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