Table 15.4 100-Coin Toss Macrostate Number of microstates Heads Tails (W) 100 99 1.0x10? 95 7.5x107 90 10 1.7×1013 75 2.4x 1023 25 60 40 1.4x 1028 55 6.1x 1028 45 51 9.9x 1028 49 50 1.0x 1029 50 49 9.9x 1028 51 45 55 6.1x1028 40 1.4x 1028 60 25 2.4x 1023 75 10 90 1.7×1013 95 7.5x107 99 1.0x102 100 Total: 1.27x1030

Table 15.4 100-Coin Toss Macrostate Number of microstates Heads Tails (W) 100 99 1.0x10? 95 7.5x107 90 10 1.7×1013 75 2.4x 1023 25 60 40 1.4x 1028 55 6.1x 1028 45 51 9.9x 1028 49 50 1.0x 1029 50 49 9.9x 1028 51 45 55 6.1x1028 40 1.4x 1028 60 25 2.4x 1023 75 10 90 1.7×1013 95 7.5x107 99 1.0x102 100 Total: 1.27x1030

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...

See similar textbooks

Related questions

Q: 5. Sarina is half as old as her mother. Twelve years ago, she was one-third of her mother's age.…

Q: 2. In a study relating college grade point average to time spent in various activities, you…

A: Given Information: Consider the given study in which the students are asked how many hours they…

Q: The stacked column graph below depicts the percentage of boys and girls in each room at the student…

Q: The population of city A is 25% less than the population of city B, so city A's population is…

Q: A county college is interested in learning what proportion of students work full-time. The registrar…

A: 6 situations are given. To choose the correct match for each one. Data: list of observation values…

Q: An experiment with three steps with 13 outcomes possible for the first step, 5 outcomes possible for…

Q: Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field…

A: From the given information, Piel has to choose four different shooting spots among the five…

Q: .In a college class, the course grade is based on: attendance, two major tests, and a final project.…

A: Solution: Given information: The score grades and there corresponfing weights are x1= 94 x2= 100x3=…

Q: A researcher uses an anonymous survey to track the number of salmon caught in Gaspe. Based on a set…

A: Given information: Sample size, n=115 Sample mean, x¯=2.3

Q: QUESTION 3. STATISTICS. An analyst in the real estate business is interested in the relationship…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: In an analysis of two attributes, if N = 1000, (A) = 100 and (B) = 300 find the frequencies of the…

Q: independent varia

A: definition:

Q: At a certain college, 32% of the students are majoring in engineering, and 55% of the students are…

A: The percentage of students in engineering (major) is 32%. The percentage of female students is 55%.…

Q: A small-business Web site contains 100 pages and 56%, 25%, and 19% of the pages contain low,…

A: Solution: Let X be the number of pages with moderate and Y be the high graphics output. From the…

Q: Data on claim amounts for central heating insurance were collected from a large portfolio of an…

A: Solution: Given observation is 200, 201, 201, 202, 209, 211, 215, 218, 228, 228, 235, 238, 262, 265,…

Q: To study the effectiveness of possible treatments for insomnia, a sleep researcher conducted a study…

A: The hypothesis test is a statistical method in which one using the sample data try to check the…

Q: What is the population of interest? O the rest of the 8,700 bricks the rest of the 8,850 bricks O…

A: Given: The total bricks are 9000 The number of bricks to be examined is 150.

Q: ey obtained a list of registered dog owners from the city of Eureka and the city of Arcata, then…

A: Given: Owners are randomly selected from each list until they had 150 responses from Arcata and 150…

Q: A survey asks: Which online services have you used in the last month: ● Twitter Facebook Have used…

Q: In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are…

A: As per guidelines expert gave to answer first question only

Q: 4. In 1983, the Department of Dairy Science at the Virginia Polytechnic Institute and State…

A: Latin square is used in the situation where the row and column with different levels. In which each…

Q: A high school tennis team is scheduled to play 28 matches. If the team wins 60% of the first 15…

Q: 1.4 1.5 1.6 Calculate if there is a surplus or deficit after the class outing. What percentage of…

Q: In a political poll, approximately 3/25 of the people asked preferred candidate A in the upcoming…

A: Given that, 3/25 of people asked preferred candidate A. The total people asked in election is…

Q: 0. The following table represents the percentages of languages studied by students at a college…

Q: The table shows the leading causes of death in a certain country in a recent year. The population of…

A: To estimate the number of deaths due to cancer, as expected from the given data

Concept explainers

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.

Question

(a) If tossing 100 coins, how many ways (microstates) are there to get the three most likely macrostates of 49 heads and 51 tails, 50 heads and 50 tails, and 51 heads and 49 tails?
(b) What percent of the total possibilities is this?

Table 15.4 100-Coin Toss
Macrostate
Number of microstates
Heads Tails
(W)
100
99
1.0x10?
95
7.5x107
90
10
1.7×1013
75
2.4x 1023
25
60
40
1.4x 1028
55
6.1x 1028
45
51
9.9x 1028
49
50
1.0x 1029
50
49
9.9x 1028
51
45
55
6.1x1028
40
1.4x 1028
60
25
2.4x 1023
75
10
90
1.7×1013
95
7.5x107
99
1.0x102
100
Total: 1.27x1030

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamental Counting Principle$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

1. A study was conducted to investigate the effects of three factors on the fragmentation of an explosive device. The factors of interest are pipe diameter, a restraint material and the air gap between the device and the restraint material. Two repeat tests were conducted on each combination of the factor levels. The data are shown below. (a) (b) (c) Air gap (C) Factors A (in.) B C (in.) Material (B) 0.50 in. 0.75 in. Factor levels Low 0.75 Sand 0.50 Sand 57.6 57.9 61.8 61.3 0.75 in. High 1.75 Earth 0.75 Pipe Diameter (A) Earth 63.2 63.5 65.8 63.5 Sand 69.5 69.2 68.1 69.0 1.75 in. Earth 69.9 62.0 55.3 59.8 Suppose that in the data above, we had confounded ABC in replicate I and AB in replicate II. Give the name of this design? Outline the design mentioned in (a). Analyze the data and infer your conclusion.
In a biology class, the final grade is based on several things: a lab score, scores on two major tests, and score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of the total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exa
B. Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field goal attempt that an offensive player can take inside of the three-point line and is worth 2 points. To practice this, Piel has to choose four different shooting spots among the five different spots in where he is comfortable of shooting. In previous games, his shot selection is 5% from the right baseline (Spot 1), 15% from the right elbow (Spot 2), 20% from the top of the key (Spot 3), 25% from the left elbow (Spot 4) and 35% from the left baseline (Spot 5). In this drill, a shooting spot can be selected once, multiple times, or not at all. This drill illustrates a random experiment with distribution. To help Piel decide, below is the partial table for the means and standard deviations of the random variable, Y, or the number of times he shoot the ball in a shooting spot. Shooting Spot E[Y] SD[Y] Spot 1 0.2 0.4359 Spot 2 0.6 0.7141 Spot 3 0.8 0.8000 Spot 4 the mean of 1.4 by will…
Probability. Please assist me in these 2 short questions.
A population starts with 16 carpet beetles and in a week the population increase by 1 new beetle for every 4 beetles that were there the previous week which can be shown in the following table: Week 0 Week 1 Week 2 Week 3 = 31 Week 5 = 49 Week 4 16 20 25 = 39 How many beetles do you estimate there will be by Week 8?
Pictured Below
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.,…
B. Perimeter Shot - A perimeter shot, also known as a mid-range shot, is a jump shot or general field goal attempt that an offensive player can take inside of the three-point line and is worth 2 points. To practice this, Piel has to choose four different shooting spots among the five different spots in where he is comfortable of shooting. In previous games, his shot selection is 5% from the right baseline (Spot 1), 15% from the right elbow (Spot 2), 20% from the top of the key (Spot 3), 25% from the left elbow (Spot 4) and 35% from the left baseline (Spot 5). In this drill, a shooting spot can be selected once, multiple times, or not at all. This drill illustrates a random experiment with distribution. To help Piel decide, below is the partial table for the means and standard deviations of the random variable, Y, or the number of times he shoot the ball in a shooting spot. Shooting Spot E[Y] SD[Y] Spot 1 0.2 0.4359 Spot 2 0.6 0.7141 Spot 3 0.8 0.8000 Spot 4 the mean of 1.4 by will…