Fatskills
Practice. Master. Repeat.
Study Guide: GED Mathematical Reasoning Quantitative Reasoning Probability Simple Probability Complementary Events
Source: https://www.fatskills.com/general-equivalency-diploma-ged/chapter/ged-mathematical-reasoning-quantitative-reasoning-probability-simple-probability-complementary-events

GED Mathematical Reasoning Quantitative Reasoning Probability Simple Probability Complementary Events

By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.

⏱️ ~6 min read

What Is This?

Simple Probability and Complementary Events are fundamental concepts in Quantitative Reasoning that help you make informed decisions under uncertainty. They enable you to calculate the likelihood of an event occurring and make predictions about outcomes.

You'll encounter these topics in exams that test your ability to analyze data, make rational decisions, and communicate complex ideas clearly. Be prepared for multiple-choice questions, short-answer questions, and essay-style questions that require you to apply these concepts to real-world scenarios.

Why It Matters

This topic appears in various exams, including the Graduate Management Admission Test (GMAT), Graduate Record Examinations (GRE), and the Law School Admission Test (LSAT). It typically carries 10-20% of the total marks and tests your ability to think critically, reason logically, and apply mathematical concepts to real-world problems.

Core Concepts

To master this topic, you must understand the following foundational ideas:


  • Simple Probability: The likelihood of an event occurring, expressed as a value between 0 and 1.
  • Complementary Events: Two events that are mutually exclusive, meaning they cannot occur at the same time.
  • Probability Rules: The laws that govern probability, including the addition rule and the multiplication rule.
  • Conditional Probability: The probability of an event occurring given that another event has occurred.

Prerequisites

Before tackling this topic, you must already understand:


  • Basic arithmetic operations, including addition, subtraction, multiplication, and division.
  • Basic algebraic concepts, including variables, equations, and functions.
  • Basic statistical concepts, including mean, median, and mode.

If you're missing these prerequisites, you'll struggle to understand the underlying logic and grammar of probability.

The Rule-Book (How It Works)

The primary rule of probability is:


  • The Probability Rule: The probability of an event occurring is equal to the number of favorable outcomes divided by the total number of possible outcomes.

Sub-rules and exceptions include:


  • The Addition Rule: The probability of two mutually exclusive events occurring is equal to the sum of their individual probabilities.
  • The Multiplication Rule: The probability of two independent events occurring is equal to the product of their individual probabilities.
  • The Complementary Rule: The probability of an event not occurring is equal to 1 minus the probability of the event occurring.

A simple visual pattern to remember is the Probability Venn Diagram, which illustrates the relationships between events and their probabilities.

Exam / Job / Audit Weighting

Frequency: 20-30% Difficulty Rating: Intermediate Question Type or Real-World Task Type: Multiple-choice questions, short-answer questions, and essay-style questions.

Difficulty Level

Intermediate

Must-Know Rules, Formulas, Standards, or Principles

The three most important rules, formulas, and principles for this topic are:


  • The Probability Rule: P(A) = Number of favorable outcomes / Total number of possible outcomes
  • The Addition Rule: P(A or B) = P(A) + P(B)
  • The Multiplication Rule: P(A and B) = P(A) × P(B)

Worked Examples (Step-by-Step)

Here are three solved examples that escalate in difficulty:

Example 1: Easy

A coin is flipped. What is the probability of getting heads? P(Heads) = 1/2

Example 2: Medium

A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? P(Red) = 5/8

Example 3: Hard

A company has two factories, A and B. Factory A produces 60% of the company's output, and factory B produces 40%. If the company's output is 100 units, how many units does factory A produce? P(A) = 0.6 P(B) = 0.4 Total output = 100 units Factory A output = P(A) × Total output = 0.6 × 100 = 60 units

Common Exam Traps & Mistakes

Here are four common errors that cost marks in exams:


  • Mistake 1: Failing to consider the complement of an event.
  • Mistake 2: Misapplying the addition rule for mutually exclusive events.
  • Mistake 3: Misapplying the multiplication rule for independent events.
  • Mistake 4: Failing to calculate the total number of possible outcomes.

Shortcut Strategies & Exam Hacks

Here are three practical techniques to solve questions faster or more accurately under time pressure:


  • Mnemonic Device: Use the Probability Venn Diagram to remember the relationships between events and their probabilities.
  • Elimination Strategy: Eliminate options that are clearly incorrect or implausible.
  • Pattern Recognition: Recognize common patterns and formulas, such as the probability rule and the addition rule.

Question-Type Taxonomy

Here are three distinct question formats that this topic appears in across different exams:


Question Format Mini-Example Exams that Favor it
Multiple-Choice What is the probability of getting heads when a coin is flipped? GMAT, GRE
Short-Answer A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? LSAT, GMAT
Essay-Style A company has two factories, A and B. Factory A produces 60% of the company's output, and factory B produces 40%. If the company's output is 100 units, how many units does factory A produce? GRE, GMAT

Practice Set (MCQs)

Here are five multiple-choice questions at mixed difficulty levels:

Question 1: Easy

What is the probability of getting heads when a coin is flipped? A) 0.5 B) 0.3 C) 0.2 D) 0.1

Correct Answer: A) 0.5


Explanation: The probability of getting heads is equal to the number of favorable outcomes (1) divided by the total number of possible outcomes (2).


Why the Distractors Are Tempting: Options B, C, and D are plausible but incorrect values.


Question 2: Medium

A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? A) 3/8 B) 5/8 C) 2/3 D) 1/2

Correct Answer: B) 5/8


Explanation: The probability of drawing a red ball is equal to the number of favorable outcomes (5) divided by the total number of possible outcomes (8).


Why the Distractors Are Tempting: Options A, C, and D are plausible but incorrect values.


Question 3: Hard

A company has two factories, A and B. Factory A produces 60% of the company's output, and factory B produces 40%. If the company's output is 100 units, how many units does factory A produce? A) 40 units B) 60 units C) 80 units D) 120 units

Correct Answer: B) 60 units


Explanation: The probability of factory A producing a unit is equal to the company's output (100 units) multiplied by the probability of factory A producing a unit (0.6).


Why the Distractors Are Tempting: Options A, C, and D are plausible but incorrect values.


Question 4: Easy

What is the probability of an event not occurring? A) 0 B) 1 C) 0.5 D) 0.8

Correct Answer: B) 1


Explanation: The probability of an event not occurring is equal to 1 minus the probability of the event occurring.


Why the Distractors Are Tempting: Options A, C, and D are plausible but incorrect values.


Question 5: Medium

A bag contains 3 red balls and 2 blue balls. What is the probability of drawing a blue ball? A) 2/5 B) 3/5 C) 1/3 D) 2/3

Correct Answer: A) 2/5


Explanation: The probability of drawing a blue ball is equal to the number of favorable outcomes (2) divided by the total number of possible outcomes (5).


Why the Distractors Are Tempting: Options B, C, and D are plausible but incorrect values.


30-Second Cheat Sheet

Here are the five things you must remember walking into the exam hall:


  • The Probability Rule: P(A) = Number of favorable outcomes / Total number of possible outcomes
  • The Addition Rule: P(A or B) = P(A) + P(B)
  • The Multiplication Rule: P(A and B) = P(A) × P(B)
  • The Complementary Rule: P(A') = 1 - P(A)
  • The Probability Venn Diagram: A visual representation of the relationships between events and their probabilities.

Learning Path

Here is a suggested study sequence to master this topic from scratch to exam-ready:


  1. Beginner Foundation: Review basic arithmetic operations, algebraic concepts, and statistical concepts.
  2. Core Rules: Study the probability rule, addition rule, multiplication rule, and complementary rule.
  3. Practice: Practice solving problems using the probability rule, addition rule, multiplication rule, and complementary rule.
  4. Timed Drills: Practice solving problems under timed conditions to improve your speed and accuracy.
  5. Mock Tests: Take mock tests to simulate the exam experience and identify areas for improvement.

Related Topics

Here are three closely connected topics that appear alongside this one in exams:


  • Conditional Probability: The probability of an event occurring given that another event has occurred.
  • Bayes' Theorem: A formula for updating probabilities based on new evidence.
  • Expected Value: A measure of the average value of a random variable.


ADVERTISEMENT