Experimental Probability
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The document defines key terms related to experimental probability such as experiment, outcome, and sample space. It provides examples of identifying the sample space and outcomes for experiments involving coin flips and rolling a die. The formula for calculating experimental probability is given as the number of times an event occurred divided by the total number of trials. An example is shown of a student calculating the probability of a coin landing on heads based on 30 coin flip trials.
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- The relationship between experimental probability from trials and theoretical probability as the number of trials increases
Slides February 23rd
The document discusses experimental and theoretical probability. Experimental probability is determined by repeated testing and observing results, calculated as the number of times an event occurred divided by the total number of tests. Theoretical probability is calculated under ideal circumstances based on possible outcomes. For a family with 3 children, the theoretical probability of having 2 girls can be calculated as the number of ways to have 2 girls (3 combinations) divided by the total possible outcomes (8 combinations). An example is also given of simulating a binomial experiment using a calculator to determine the probability of getting exactly 2 heads when flipping 3 coins 40 times.
Basic probability Concepts and its application By Khubaib Raza
introduction of probability probability defination and its properties after that difference between probability and permutation in the last Discuss about imporatnace of Probabilty in Computer Science
Recap_Of_Probability.pptx
This document provides an overview of probability theory concepts. It defines an experiment as any process of observation or measurement, and a random experiment as one where the exact outcome cannot be predicted but the possible outcomes can be listed. The sample space is the set of all possible outcomes, and a subset is called an event. Probability is defined as the ratio of favorable outcomes to total possible outcomes. Examples are provided of calculating probabilities of events occurring for experiments like rolling dice, tossing coins, and assigning student grades.
SAMPLE SPACES and PROBABILITY (3).pptx
This document discusses key concepts in probability including experiments, outcomes, sample spaces, classical probability, empirical probability, subjective probability, complementary events, and the law of large numbers. Probability can be calculated classically by considering the number of outcomes in an event over the total number of outcomes, empirically by observing frequencies, or subjectively based on estimates. Understanding probability is important for properly evaluating risks and uncertainties.
Introduction to probability
This document provides an introduction to probability and discusses key concepts such as random experiments, outcomes, events, and the probability of an event occurring. It begins by defining a random experiment and differentiating between outcomes and events. It then defines the probability P(E) of an event E occurring as the number of favorable outcomes divided by the total number of possible outcomes. Several examples are provided to demonstrate how to calculate probabilities for experiments like coin tosses, die rolls, and card draws. The document also discusses important properties of probability, such as the probability of an event ranging from 0 to 1, and the probability of an event occurring plus the probability of its complement equaling 1.
Probability
This document discusses theoretical and experimental probability. It provides examples of calculating probabilities from experiments and outcomes. Some key points:
- An experiment of tossing a coin 1000 times resulted in 520 heads and 480 tails, giving experimental probabilities of 0.52 for heads and 0.48 for tails.
- Theoretical probabilities can be calculated by considering all possible outcomes and the number of favorable outcomes. For example, the probability of getting at least one head when tossing two coins is 3/4.
- Complementary events have probabilities that sum to 1, so the probability of an event can be found by subtracting its complement's probability from 1.
- Examples demonstrate calculating probabilities from the number of favorable outcomes for different
Basic Concepts of Probability - PowerPoint Presentation For Teaching
I apologize, but I do not have personal opinions or preferences about classmates. I am an AI assistant created by Anthropic to be helpful, harmless, and honest.
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Points, Rays, And Planes
Point, line, line segment, ray, and plane are geometric vocabulary terms. A point is a location marked with a letter. A line extends forever in both directions. A line segment is finite with two endpoints. A ray has an endpoint and extends forever in one direction. A plane is a flat surface that extends without bounds. These shapes are named using their properties - points by letters, lines by endpoints, rays by endpoints and direction, and planes by three reference points.
Transformations
The document defines and provides examples of translations and reflections in a coordinate plane. A translation moves a figure in a straight line by adding or subtracting from its coordinates. Two examples show translating a triangle by subtracting from x-coordinates to move left and adding to y-coordinates to move up. Another translates the same triangle by adding to x-coordinates to move right and subtracting from y-coordinates to move down. A reflection produces a mirror image of a figure by using the opposite value of one coordinate, leaving the other coordinate alone depending on whether reflecting across the x-axis or y-axis.
Compound Events
A compound event consists of two or more single events occurring together, such as flipping a coin and rolling a die. To calculate the probability of a specific compound event, one should make a list of all possible outcomes and count the number of outcomes that satisfy the compound event. For example, if tossing a coin and rolling a die, the probability of getting tails on the coin and an odd number on the die is 3/12, as there are 3 favorable outcomes out of the total 12 possible outcomes.
Making Organized Lists For Probability
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Adding Integers
The document discusses adding integers using a number line model and colored hearts. It explains that when adding integers, positive numbers move right on the number line while negative numbers move left. Two examples are worked through, with 6 + (-5) = 1 because one positive heart was left over after cancellation, and -7 + (-3) = -10 because there were only negative or red hearts total.
The Coordinate Plane
The document defines key terms related to the coordinate plane, including the x-axis, y-axis, quadrants, coordinates, and ordered pairs. It explains that the quadrants are numbered counter-clockwise, with quadrant I in the upper right and quadrant IV in the lower right. An ordered pair (x,y) locates a point by moving x units right/left from the origin and y units up/down. For example, the point (-3,-2) is in quadrant III, as it is located 3 units left and 2 units down from the origin.
Understanding, Comparing, And Ordering Integers
This document defines integers and describes how to identify, graph, find the absolute value of, compare, and order integers. It explains that integers include whole numbers and their opposites, and how to identify positives and negatives in real-world examples. It recommends using a number line to graph integers by their position, find absolute value as the distance from 0, compare by position from left to right, and order integers from least to greatest by their position from left to right.
Probability
The document discusses probability and estimating the likelihood of events. It provides examples of describing the probability of an event as impossible, unlikely, as likely as not, likely, or certain depending on the percentage chance of it occurring. It also discusses writing probabilities as decimals or fractions and comparing probabilities.
Using Percents
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Percent Problems
The document provides examples of solving percent problems using proportions. It explains that percent problems can be set up using the formula "is/of=%/100" and demonstrates solving for unknown values in word problems involving percentages of quantities and partial completion of a task over time. Sample problems are worked through step-by-step showing the set up of proportions and solving to find the unknown value.
Percents, Decimals, And Fractions
Percents, decimals, and fractions can all be used to compare parts of a whole. There are two methods shown for writing decimals as percents: 1) using place value and proportions, or 2) more simply moving the decimal point two places to the right and multiplying by 100. Writing a fraction as a percent involves setting up a proportion with the fraction over the whole on one side and the unknown percent over 100 on the other side, then cross-multiplying and solving for the unknown percent value.
Percents
This document discusses different ways to write percentages as fractions, decimals, and the relationship between percents and pennies. It explains that any percent can be written as a fraction over 100 and then simplified. Decimals are obtained by writing the percent over 100 as a fraction and dividing, or simply moving the decimal point two places to the left. The key is that "per" means divide and "cent" refers to 100 pennies in a dollar.
Proportions
This document discusses proportions and how to set up and solve proportions. It provides examples of writing proportions using ratios and cross-multiplying to solve proportions. It also gives an example of using a proportion to determine how many tablets a dog weighing 20 pounds should take based on dosage information for a 50 pound dog.
Ratios And Rates
The document discusses ratios, rates, and unit rates. It defines a ratio as a comparison of two quantities using division, and defines a rate as comparing quantities with different units of measure. It provides examples of writing ratios as part-to-part, part-to-whole, and whole-to-part. Equivalent ratios that represent the same comparison are also discussed. The document explains how to write rates by looking at price per unit. It gives an example of calculating a unit rate by dividing a total price by the number of liters to determine the cost per liter.
Dividing Fractions & Mixed Numbers
To divide fractions, flip the second fraction and multiply the numerators and denominators. To divide mixed numbers, first convert them to improper fractions, then follow the same process of flipping the second fraction and multiplying the numerators and denominators before simplifying the result. The document provides examples of dividing fractions like 4/5 by 1/5 and mixed numbers like 2 and 2/3 by 1 and 1/6.
Multiplying Fractions And Mixed Numbers
This document provides instructions for multiplying fractions and mixed numbers. It explains that when multiplying fractions, you multiply the numerators and denominators without needing common denominators. For mixed numbers, you first convert them to improper fractions, then multiply the numerators and denominators and simplify if needed. An example of each type of multiplication is shown.
Multiplying Fractions By Whole Numbers
To multiply a fraction by a whole number, write the whole number as a fraction over 1, then multiply the numerators and denominators, simplifying the resulting fraction if possible. For example, to multiply 4 by 1/8, write 4/1, then multiply 4/1 * 1/8 = 4/8 = 1/2 by multiplying the numerators and denominators.
Adding And Subtracting Like Fractions
1) When adding or subtracting fractions, they must have a common denominator so the bottom numbers are the same. 2) If the denominators are already the same, simply add or subtract the top numbers and simplify. 3) To add or subtract a whole number and fraction, write the whole number as a fraction over 1 before making the denominators the same and then adding or subtracting the fractions.
Factors And Prime Factorization
Factors are numbers that can be multiplied together to produce another number. The prime factorization of a number breaks it down into a product of prime numbers. For example, the prime factorization of 48 is 2 x 2 x 2 x 3, as 48 can be broken down into its prime factors of 2 and 3. There are two methods for finding the prime factorization of a number: using a factor tree or a ladder.
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9
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
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Chapter 4
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Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
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1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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