Decide whether the exercise involves permutations or combinations, and then solve the problem. Marbles are being drawn without replacement from a bag containing 13 marbles. (a) How many samples of 3 marbles can be drawn? (b) How many samples of 4 marbles can be drawn? (c) If the bag contains 2 yellow, 3 white, and 8 blue marbles, how many samples of 2 marbles can be drawn in which all marbles are blue?

Decide whether the exercise involves permutations or combinations, and then solve the problem. Marbles are being drawn without replacement from a bag containing 13 marbles. (a) How many samples of 3 marbles can be drawn? (b) How many samples of 4 marbles can be drawn? (c) If the bag contains 2 yellow, 3 white, and 8 blue marbles, how many samples of 2 marbles can be drawn in which all marbles are blue?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Please answer all three parts of this question. 1. You are designing a 2x3 factorial design and need 20 participants in each of 6 conditions. How many participants in total would be needed for a 2x3 independent groups (between-subjects) design? How many participants in total would be needed for a 2x3 repeated-measure groups (within-subjects) design? How many participants in total would be needed for a 2x3 mixed factorial design?
A friend of mine is giving a dinner party. His current wine supply includes 7 bottles of zinfandel, 11 of merlot, and 13 of cabernet (he only drinks red wine), all from different wineries. (a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (b) If 6 bottles of wine are to be randomly selected from the 31 for serving, how many ways are there to do this? (c) If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? (d) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (Round your answer to three decimal places.) (e) If 6 bottles are randomly selected, what is the probability that all of them are the same variety? (Round your answer to three decimal places.)
It has been discovered that a sub-species of animal, the Spotted Manumar, has 4 different blood types: M, N, P and MN. Type MN is uncommon: Only 10% of them have this type. The remaining 90% of the animals are equally split among the 3 other types. On another continent, there is another sub-species of the Manumar. The Furry Manumar also has the same 4 blood types and the researchers wonder if the proportions of bloodtypes matches that of the Spotted ones. If we hypothesized that the Furry ones did match the Spotted ones, and 200 Furry Manumars were to be collected at random, you'd expect the number that have bloodtype MN to be 1 and the number to have bloodtype M to be
In a survey, it was found that 80% of adults operate the flusher of toilets in public restrooms with their foot. (a) If 300 adults are randomly selected, how many would we expect to flush toilets in public restrooms with their foot? (b) Would it be unusual to observe 255 adults who flush toilets in public restrooms with their foot? (a) We would expect (Type a whole number.) adults to flush toilets in public restrooms with their foot. (b) Would it be unusual to observe 255 adults who flush toilets in public restrooms with their foot? Choose the correct answer below. O A. Yes, because 255 is greater than u + 2o. O B. No, because 255 is greater than u + 20. O C. Yes, because 255 is between u - 20 and u+ 20. O D. No, because 255 is less than u- 20. O E. No, because 255 is between u -20 and u+ 20.
In a class there are 4 students who are 19 years old and obtained 80 pints in the midterm. There are 6 students who are 19 years old and obtained 50 pints in the midterm. There are 6 students who are 20 years old and obtained 80 pints in the midterm. There are n students who are 20 years old and obtained 50 pints in the midterm. There are no other students. We randomly pick a student in the class, let their age be X and their score by Y. If we are given that X, Y are independent random variables, then compute n.
A manufacturing plant makes computer chips 24 hours a day. Employees work one of three, 8 hour shifts during the morning (2am-10am), day (10am-6pm), and night (6pm-2am). Below are data on the number of defective chips on a randomly chosen 24 hour period. Shift Morning Day Night Number of Defective Chips 23 26 47 Total Chips Manufactured 330 330 330 The plant manager thinks there might be more defective computer chips manufactured during the night shift compared to the day shift. Give appropriate statistical evidence to test the managers' claim.
1. For her botany class project, Jennifer wonders if there is a connection between the average weight of watermelons a vine produces and the root depth of the vine. Jennifer suspects that vines with deeper roots have a better water supply and produce larger melons. From a large watermelon field, 10 vines are chosen at random. At the end of 8 weeks, the watermelons are removed from each vine and the average weight of the watermelons from each vine is determined. Each plant is carefully dug up and its root depth (or length) is measure. Let x represent the root depth (to the nearest inch) and y be the mean weight of the watermelons on the vine (in pounds). Suppose that x = 17, s, = 6, y = 12, s, = 5.1, and r = = 0.93. a. Find the equation of the least squares regression line (round a and b to the nearest tenth). b. List 2 points that you know will be on the least-squares line you found in part a. c. What percent of variation is accounted for by a linear relationship? d. Using part a.,…