StudySmarter: Study help & AI tools

4.5 • +22k Ratings

More than 22 Million Downloads

Free

Addition Rule of Probability

Delve into the fascinating world of engineering mathematics with a comprehensive exploration of the Addition Rule of Probability. This pivotal mathematical concept has a wide range of applications from data analysis in the engineering field to making informed decisions in day-to-day life. Get ready to acquire a robust understanding of its meaning, properties, real-world applications and the formularic intricacies. The article further escalates its practicality with multiple examples, detailed solutions, and even complex scenarios involving the addition and multiplication rules of probability. An essential read for anyone seeking proficiency in understanding and applying the Addition Rule of Probability – from beginner to advanced level.

Explore our app and discover over 50 million learning materials for free.

- Design Engineering
- Engineering Fluid Mechanics
- Engineering Mathematics
- Acceptance Sampling
- Addition Rule of Probability
- Algebra Engineering
- Application of Calculus in Engineering
- Area under curve
- Basic Algebra
- Basic Derivatives
- Basic Matrix Operations
- Bayes' Theorem
- Binomial Series
- Bisection Method
- Boolean Algebra
- Boundary Value Problem
- CUSUM
- Cartesian Form
- Causal Function
- Centroids
- Cholesky Decomposition
- Circular Functions
- Complex Form of Fourier Series
- Complex Hyperbolic Functions
- Complex Logarithm
- Complex Trigonometric Functions
- Conservative Vector Field
- Continuous and Discrete Random Variables
- Control Chart
- Convergence Engineering
- Convergence of Fourier Series
- Convolution Theorem
- Correlation and Regression
- Covariance and Correlation
- Cramer's rule
- Cross Correlation Theorem
- Curl of a Vector Field
- Curve Sketching
- D'alembert Wave Equation
- Damping
- Derivative of Polynomial
- Derivative of Rational Function
- Derivative of a Vector
- Directional Derivative
- Discrete Fourier Transform
- Divergence Theorem
- Divergence Vector Calculus
- Double Integrals
- Eigenvalue
- Eigenvector
- Engineering Analysis
- Engineering Graphs
- Engineering Statistics
- Euler's Formula
- Exact Differential Equation
- Exponential and Logarithmic Functions
- Fourier Coefficients
- Fourier Integration
- Fourier Series
- Fourier Series Odd and Even
- Fourier Series Symmetry
- Fourier Transform Properties
- Fourier Transform Table
- Gamma Distribution
- Gaussian Elimination
- Half Range Fourier Series
- Higher Order Integration
- Hypergeometric Distribution
- Hypothesis Test for a Population Mean
- Implicit Function
- Improved Euler Method
- Interpolation
- Inverse Laplace Transform
- Inverse Matrix Method
- Inverse Z Transform
- Jacobian Matrix
- Laplace Shifting Theorem
- Laplace Transforms
- Large Sample Confidence Interval
- Least Squares Fitting
- Logic Gates
- Logical Equivalence
- Maths Identities
- Maxima and Minima of functions of two variables
- Maximum Likelihood Estimation
- Mean Value and Standard Deviation
- Method of Moments
- Modelling waves
- Multiple Regression
- Multiple Regression Analysis
- Newton Raphson Method
- Non Parametric Statistics
- Nonlinear Differential Equation
- Nonlinear Regression
- Numerical Differentiation
- Numerical Root Finding
- One Way ANOVA
- P Value
- Parseval's Theorem
- Partial Derivative
- Partial Derivative of Vector
- Partial Differential Equations
- Particular Solution for Differential Equation
- Phasor
- Piecewise Function
- Polar Form
- Polynomial Regression
- Probability Engineering
- Probability Tree
- Quality Control
- RMS Value
- Radians vs Degrees
- Rank Nullity Theorem
- Rank of a Matrix
- Reliability Engineering
- Runge Kutta Method
- Scalar & Vector Geometry
- Second Order Nonlinear Differential Equation
- Simple Linear Regression Model
- Single Sample T Test
- Standard Deviation of Random Variable
- Superposition
- System of Differential Equations
- System of Linear Equations Matrix
- Taylor's Theorem
- Three Way ANOVA
- Total Derivative
- Transform Variables in Regression
- Transmission Line Equation
- Triple Integrals
- Triple Product
- Two Sample Test
- Two Way ANOVA
- Unit Vector
- Vector Calculus
- Wilcoxon Rank Sum Test
- Z Test
- Z Transform
- Z Transform vs Laplace Transform
- Engineering Thermodynamics
- Materials Engineering
- Professional Engineering
- Solid Mechanics
- What is Engineering

Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenDelve into the fascinating world of engineering mathematics with a comprehensive exploration of the Addition Rule of Probability. This pivotal mathematical concept has a wide range of applications from data analysis in the engineering field to making informed decisions in day-to-day life. Get ready to acquire a robust understanding of its meaning, properties, real-world applications and the formularic intricacies. The article further escalates its practicality with multiple examples, detailed solutions, and even complex scenarios involving the addition and multiplication rules of probability. An essential read for anyone seeking proficiency in understanding and applying the Addition Rule of Probability – from beginner to advanced level.

The Addition Rule of Probability is a concept in probability theory that allows you to calculate the probability of two events occurring together.

The Simple Addition Rule of Probability applies when you have mutually exclusive events. In this context, mutually exclusive events are those that cannot occur at the same time.

The General Addition Rule of Probability applies when the events are not mutually exclusive, meaning they can occur simultaneously.

Suppose you are undertaking a major construction project. The probabilities of encountering two major risks - encountering unstable geological conditions and facing labor strikes - have been computed separately. However, if these risks are not mutually exclusive (perhaps labor strikes are more likely in difficult working conditions), you'll need to use the General Addition Rule of Probability to calculate the total risk probability.

Did you know? Google's search algorithm, PageRank, actually makes use of probability to determine the importance of web pages, factoring in the "probability" that a user will click on a particular link. This probability computation not only matches the search query terms but also considers the relevance and quality of web pages, demonstrating the significance of probability in computer science.

- If A and B are mutually exclusive (one event's occurrence doesn't affect the other's), the formula is straightforward: the probability of either A or B occurring is the sum of their individual probabilities.
- If A and B can occur simultaneously, the formula includes a third term: the intersection of A and B, denoting the probability of both A and B occurring together.

Mathematical Variables |
Description |

P(A) | Probability of event A happening |

P(B) | Probability of event B happening |

P(A \cup B) | Probability of either event A or B happening |

P(A \cap B) | Probability of both events A and B happening together |

- Event A: Drawing a heart
- Event B: Drawing a queen

- Use the Addition Rule if you’re analysing two or more events occurring separately or together.
- Use the Multiplication Rule if you’re addressing two or more events happening in sequence.

- Use the Addition Rule to calculate the probability of the first event - drawing a red card.
- Apply the Multiplication Rule to find the probability of the second event - drawing a king, considering one red card has been removed.
- Apply the Multiplication Rule again to find the probability of drawing a heart, considering a red card and a king have been removed.
- The final answer is the multiplication of the three probabilities found in the previous steps.

- Mutually exclusive events in probability are those that cannot happen at the same time. For mutually exclusive events, the Simple Addition Rule of Probability applies, which is expressed as P(A ∪ B) = P(A) + P(B).
- Non-mutually exclusive events in probability are those that can occur together. For such events, the General Addition Rule of Probability is used, which is expressed as P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
- The Addition Rule of Probability has practical applications in real-life scenarios such as risk assessment in engineering projects, computing and information technology, data analysis, and machine learning.
- The formula for the Addition Rule of Probability changes depending on whether events A and B are mutually exclusive or can occur simultaneously. The symbol ∪ represents "union" which implies 'either A or B', and ∩ indicates "intersection", which refers to 'both A and B'.
- The Addition and Multiplication Rules of Probability are foundational pillars in the study of probability. The Addition Rule is used when analysing two or more events occurring separately or together. The Multiplication Rule is used when addressing two or more events happening in sequence.

The Addition Rule of Probability can be proven using a Venn diagram or set theory. First, represent the events as sets. The probability of either event occurring is the sum of their individual probabilities minus the intersection (if events are not mutually exclusive). This demonstrates that P(A∪B) = P(A) + P(B) - P(A∩B).

The Addition Rule of Probability in Engineering Mathematics states that the probability of the occurrence of at least one of two or more mutually exclusive events is the sum of their individual probabilities. This rule is essential in probability and statistical analysis.

The Addition Rule of Probability, also known as the 'OR' rule, has two fundamental properties: 1) For mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities; 2) For non-mutually exclusive events, the probability of either event occurring is the sum of their individual probabilities minus the probability of their intersection.

The formula for the Addition Rule of Probability is P(A∪B) = P(A) + P(B) - P(A∩B). This equation provides the probability of either event A or event B (or both) occurring.

One example is calculating the probability of rolling a 3 or 4 on a six-sided die (1/6 + 1/6). Another is the chance of picking a red or a blue marble from a bag that contains different coloured marbles. Lastly, the likelihood of drawing a king or a queen from a deck of cards.

What is the basic formula for the Addition Rule of Probability?

The Addition Rule of Probability states that the probability of the occurrence of two mutually exclusive events A and B is the sum of the probabilities of the individual events, simply put, P(A ∪ B) = P(A) + P(B).

How does the Addition Rule of Probability change when events are not mutually exclusive?

If events A and B are not mutually exclusive, meaning they can both occur simultaneously, the Addition Rule modifies to: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

How does the Addition Rule of Probability differ from the Multiplication Rule of Probability?

The Addition Rule of Probability focuses on the 'or' operator, calculating the probability of either event A or B occurring. In contrast, the Multiplication Rule of Probability uses the 'and' operator, estimating the probability of both events A and B occurring together.

What is the addition rule of probability for mutually exclusive events?

For mutually exclusive events, the probability of either occurrence is the sum of their individual probabilities, expressed as P(A ∪ B) = P(A) + P(B).

How does the addition rule of probability adjust for non-mutually exclusive events?

For non-mutually exclusive events, the addition rule accounts for the intersection of the events, given as P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

In what way does the addition rule of probability deal with independent events?

For independent events, the intersection becomes the multiplication of their probabilities, making the addition rule appear as P(A ∪ B) = P(A) + P(B) - P(A)P(B).

Already have an account? Log in

Open in App
More about Addition Rule of Probability

The first learning app that truly has everything you need to ace your exams in one place

- Flashcards & Quizzes
- AI Study Assistant
- Study Planner
- Mock-Exams
- Smart Note-Taking

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in