# Probability Models

#### Grade 7 Math Worksheets

Probability models are mathematical models that are used to describe and analyze the likelihood of different events.

Table of Contents:

- Probability Models
- Discrete Probability Models
- Continuous Probability Models
- Binomial Distribution
- Poisson Distribution
- Geometric Distribution
- FAQs

**Personalized Online Tutoring**

## Probability Models - Grade 7 Math Worksheet PDF

This is a free worksheet with practice problems and answers. You can also work on it online.

Sign up with your email ID to access this free worksheet.

### "We really love eTutorWorld!"

*"We really love etutorworld!. **Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)*

### "My daughter gets distracted easily"

*"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.*

* With the help of Etutorworld, my daughter has been now selected in *

*the*

**Gifted and Talented Program**for the school district"*- Nivea Sharma (via TrustSpot.io)*

**Probability Models**

Probability models are mathematical models that are used to describe and analyze the likelihood of different events. They are often used in probability theory and statistics to make predictions, estimate probabilities, and simulate outcomes of experiments or random events.

### Some common types of probability models include:

**Discrete probability models:** These models are used to describe random events with a finite or countable number of possible outcomes. Examples include flipping a coin, rolling a die, or drawing cards from a deck.

**Continuous probability models:** These models are used to describe random events with an infinite number of possible outcomes. Examples include measuring the height of a person or the time it takes for a car to stop.

**Binomial distribution:** This is a discrete probability model that is used to describe the probability of a certain number of successes in a fixed number of independent trials. For example, the number of heads that will occur in 10 coin flips.

**Normal distribution:** This is a continuous probability model that is used to describe the distribution of many naturally occurring phenomena, such as height, weight, and IQ scores. It is also used in statistical hypothesis testing and confidence intervals.

**Poisson distribution:** This is a discrete probability model that is used to describe the probability of a certain number of events occurring in a fixed time interval, assuming that the events occur randomly and independently. For example, the number of phone calls received in a day at a call center.

Probability models are used in a wide range of fields, including finance, engineering, biology, and social sciences. They help us to make informed decisions and predictions based on the likelihood of different outcomes.

### Discrete Probability Models

Discrete probability models are used to describe random events with a finite or countable number of possible outcomes. In a discrete probability model, the probability of each possible outcome is defined, and the sum of all probabilities is equal to 1.

#### Some common examples of discrete probability models include:

**Bernoulli distribution:** This is a discrete probability model that is used to describe the probability of a single event with two possible outcomes, such as flipping a coin or rolling a die. The two outcomes are usually denoted as “success” and “failure,” and the probability of success is denoted as p.

**Binomial distribution:** This is a discrete probability model that is used to describe the probability of a certain number of successes in a fixed number of independent trials. For example, the number of heads that will occur in 10 coin flips. The binomial distribution is defined by two parameters: the probability of success p and the number of trials n.

**Poisson distribution:** This is a discrete probability model that is used to describe the probability of a certain number of events occurring in a fixed time interval, assuming that the events occur randomly and independently. For example, the number of phone calls received in a day at a call center. The Poisson distribution is defined by one parameter: the average number of events in the time interval.

**Geometric distribution:** This is a discrete probability model that is used to describe the probability of the number of trials required to achieve the first success in a sequence of independent trials. For example, the number of times a coin needs to be flipped until the first head appears. The geometric distribution is defined by one parameter: the probability of success p.

Discrete probability models are used in a wide range of applications, including quality control, risk analysis, and decision-making. They help us to understand the likelihood of different outcomes and make informed decisions based on probability.

### Continuous Probability Models

Continuous probability models are used to describe random events with an infinite number of possible outcomes. In a continuous probability model, the probability of each possible outcome is defined by a probability density function (PDF), which gives the probability density at each point in the range of possible outcomes.

#### Some common examples of continuous probability models include:

**Normal distribution:** This is a continuous probability model that is used to describe the distribution of many naturally occurring phenomena, such as height, weight, and IQ scores. It is also used in statistical hypothesis testing and confidence intervals. The normal distribution is defined by two parameters: the mean, which represents the center of the distribution, and the standard deviation, which represents the spread of the distribution.

**Exponential distribution:** This is a continuous probability model that is used to describe the time between events in a Poisson process, where events occur randomly and independently over time. For example, the time between customer arrivals at a store or the time between machine failures in a factory. The exponential distribution is defined by one parameter: the rate, which represents the average number of events per unit time.

**Uniform distribution:** This is a continuous probability model that is used to describe random events where every outcome in a given range is equally likely. For example, the height of a randomly selected person from a certain population or the time it takes to complete a task. The uniform distribution is defined by two parameters: the minimum and maximum values of the range.

**Beta distribution:** This is a continuous probability model that is used to describe probabilities for events that have a limited range, such as proportions or percentages. For example, the probability that a certain product will be purchased or the likelihood of success in a medical treatment. The beta distribution is defined by two parameters: alpha and beta.

Continuous probability models are used in a wide range of fields, including finance, engineering, biology, and social sciences. They help us to make informed decisions and predictions based on the likelihood of different outcomes.

### Binomial Distribution

The binomial distribution is a discrete probability distribution that is commonly used to model the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant for all trials. The binomial distribution is denoted by the notation B(n, p), where n is the number of trials and p is the probability of success.

The probability of getting exactly k successes in n independent trials with probability of success p is given by the binomial probability formula:

**P(X = k) = (n choose k) * p^k * (1-p)^(n-k)**

where (n choose k) represents the binomial coefficient, which is the number of ways to choose k objects from a set of n objects. The formula can be read as follows: the probability of k successes is equal to the number of ways to choose k successes from n trials, multiplied by the probability of k successes and (n-k) failures occurring, where the probability of success is p and the probability of failure is (1-p).

The mean (expected value) and variance of the binomial distribution are given by:

Mean: E(X) = np

Variance: Var(X) = np(1-p)

The binomial distribution is commonly used in many applications, including quality control, polling, and genetics. For example, a manufacturer may use the binomial distribution to determine the probability of producing a certain number of defective items in a batch of products, or a pollster may use the binomial distribution to determine the probability of a certain number of people voting for a particular candidate in an election.

*“**There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt. *

*Our kid is doing much better with a higher score.**”*

### 7th Grade Tutoring

eTutorWorld offers **Personalized Online Tutoring** for Math, Science, English, and Standardised Tests.

Our Tutoring Packs start at just under** $21 per hour**, and come with a moneyback guarantee.

**Schedule a FREE Trial Session**, and experience quality tutoring for yourself. (No credit card required.)

### Poisson Distribution

The Poisson distribution is a discrete probability distribution that is used to model the number of occurrences of an event in a fixed interval of time or space, given the average rate of occurrence. The Poisson distribution is named after French mathematician Siméon Denis Poisson.

The Poisson distribution is denoted by the notation P(λ), where λ is the average rate of occurrence of the event in a given interval of time or space. The probability of getting exactly k occurrences in the interval is given by the Poisson probability formula:

**P(X=k) = (e^(-λ) * λ^k) / k!**

where e is the mathematical constant approximately equal to 2.71828 and k! represents the factorial of k.

The mean (expected value) and variance of the Poisson distribution are both equal to λ.

The Poisson distribution is commonly used in many applications, including:

Counting the number of accidents, crimes, or defects in a given period of time or space

Analyzing the number of customers arriving at a service desk or in a queue

Modeling the number of mutations in a DNA sequence

Analyzing the number of radioactive decay events in a sample

Analyzing the number of calls arriving at a call center

The Poisson distribution is closely related to the binomial distribution, where the number of trials is very large and the probability of success is very small. When n is large and p is small, the binomial distribution can be approximated by the Poisson distribution with λ = np.

### Geometric Distribution

The geometric distribution is a discrete probability distribution that models the number of independent trials needed to obtain the first success in a sequence of trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant for all trials. The geometric distribution is denoted by the notation Geo(p), where p is the probability of success.

The probability of getting the first success on the kth trial is given by the geometric probability formula:

**P(X = k) = (1 – p)^(k-1) * p**

where k is the number of trials needed to obtain the first success.

The mean (expected value) and variance of the geometric distribution are given by:

Mean: E(X) = 1/p

Variance: Var(X) = (1-p) / p^2

The geometric distribution is commonly used in many applications, including:

Analyzing the number of attempts needed to win a game

Analyzing the number of phone calls needed to get a sale

Analyzing the number of attempts needed to pass a driving test

Analyzing the number of attempts needed to solve a puzzle

The geometric distribution is related to the binomial distribution, where the number of trials is fixed and the probability of success is small. When n is large and p is small, the binomial distribution can be approximated by the geometric distribution.

### Do You Stack Up Against the Best?

If you have 30 minutes, try our free diagnostics test and assess your skills.

## Probability Models FAQS

##### What is a probability model?

A probability model is a mathematical framework used to describe the probability distribution of a random variable or a set of random variables. It is used to make predictions about the likelihood of certain events or outcomes based on known or assumed probabilities.

##### What are the different types of probability models?

There are two main types of probability models: discrete and continuous. Discrete probability models are used to model situations where the outcomes are countable, such as rolling a dice or flipping a coin. Continuous probability models are used to model situations where the outcomes are uncountable, such as measuring the height or weight of a person.

##### What are the most commonly used discrete probability models?

The most commonly used discrete probability models are the binomial distribution, the Poisson distribution, and the geometric distribution. These models are used to describe the probability distribution of the number of occurrences of a certain event.

##### What are the most commonly used continuous probability models?

The most commonly used continuous probability models are the normal distribution, the exponential distribution, and the uniform distribution. These models are used to describe the probability distribution of a continuous random variable.

##### What is the difference between a probability distribution function and a cumulative distribution function?

A probability distribution function (PDF) is a function that describes the probability distribution of a random variable. It gives the probability of a certain value of the variable occurring. A cumulative distribution function (CDF) gives the probability that a random variable is less than or equal to a certain value. The CDF is the integral of the PDF.

##### What is the expected value of a probability model?

The expected value of a probability model is the long-run average of the values that the random variable takes. It is the weighted average of the possible outcomes of the random variable, where the weights are the probabilities of each outcome.

##### What is the variance of a probability model?

The variance of a probability model measures the spread or variability of the probability distribution around the expected value. It is the expected value of the squared deviation of the random variable from its expected value.

**Gloria Mathew** writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

### Affordable Tutoring Now Starts at Just $21

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).

What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.

Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a **FREE TRIAL **Session with us today.

**There is no purchase obligation or credit card requirement*

## Grade 7 Science Worksheets

- Elements and Compounds
- Solar Energy
- Photosynthesis
- Electricity and Magnetism
- Law of conservation of energy
- Periodic table
- Properties of Matter
- Waves
- Energy Resources
- Weather and Climate
- Immune, Circulatory and Digestive Systems
- Organs in Multi-cellular Organism
- Sedimentary, Igneous, and Metamorphic Rocks
- Structure of the Earth
- Law of Conservation of Mass
- Physical and Chemical Changes
- Scientific Method
- Human Digestive System
- Environmental Science
- Renewable and Non-renewable energy Resources
- Characteristics of Living Organisms
- Life Science
- Earth and Space Science
- Solar Eclipse
- Heat Technology
- Newton’s Laws of Motions
- Physical Science
- Tools, Measurement and SI Units
- Earth Atmosphere
- Interactions of Living things
- The Earth Ecosystem
- Organelles in Plant and Animal cells
- Layers of the Earth
- Cycles in Nature

## Grade 7 Math Worksheets

- Fractions
- Linear equations word problems
- Statistics
- Properties of Parallel Line
- Finding slope from an equation
- Identifying Quadrilaterals
- Percent Change
- Properties of addition and multiplication
- Pythagorean Theorem
- Solving two step inequalities
- Symmetry
- Fractions to Decimals (New)
- Whole Number Exponents with Integer Bases (New)
- Adding and Subtracting Fractions (New)
- Integer Addition and Subtraction (New)
- Dividing Mixed Numbers (New)
- Basics of Coordinate Geometry (New)

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.

**Online test prep and practice**

SCAT

CogAT

SSAT

ISEE

PSAT

SAT

ACT

AP Exam

**Science Tutoring**

Physics Tutoring

Chemistry Tutoring

Biology Tutoring

**Math Tutoring**

Pre-Algebra Tutoring

Algebra Tutoring

Pre Calculus Tutoring

Calculus Tutoring

Geometry Tutoring

Trigonometry Tutoring

Statistics Tutoring

**Quick links**

Free Worksheets

Fact sheet

Sales Partner Opportunities

Parents

Passive Fundraising

Virtual Fundraising

Our Expert Tutors

Safe and Secure Tutoring

Interactive Online Tutoring

After School Tutoring

Elementary School Tutoring

Middle School Tutoring

High School Tutoring

Home Work Help

Math Tutors New York City

Press

©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird

©2022 eTutorWorld

Terms of use

Privacy Policy

Site by Little Red Bird