Short Tricks to deal with cases of 'At least' & 'At most'

Duration: 9 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-SENIOR-COMPUTER-INSTRUCTOR/paper-1-basic-numeracy/probability/classical-problems-cards-dice-coins-digits-number-objects/asset-short-tricks-to-deal-with-cases-of-at-least-at-most after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video, presented by Yash Jain from Knowledge Gate, provides a step-by-step solution to a probability problem. The core of the lesson is the calculation of probabilities for different outcomes when a coin is tossed twice. The instructor begins by defining the sample space, which consists of four equally likely outcomes: HH, HT, TH, and TT. He then systematically addresses three parts of the question: (i) the probability of getting exactly one head, (ii) the probability of getting at least one head, and (iii) the probability of getting at most one head. For each part, he identifies the favorable outcomes from the sample space and applies the fundamental formula for probability: P(E) = (Number of favorable outcomes) / (Total number of outcomes). The video demonstrates the direct calculation method and also shows how to use the complement rule for part (ii), where P(at least one head) = 1 - P(no heads). The visual presentation uses a digital whiteboard with handwritten text and diagrams to clearly illustrate the problem-solving process.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide featuring the word "PROBABILITY" in a purple box, surrounded by four images: a casino table with dice, a basket of fruit, a pizza box, and a business meeting. The scene then transitions to the main lecture slide, which has a pink background with a word cloud. The title "PROBABILITY" is displayed at the top, and the instructor, Yash Jain, is shown in a small window in the bottom right corner. The slide introduces the problem: "A coin is tossed twice. Find the probability of getting:" followed by three sub-questions: (i) exactly one head, (ii) at least one head, and (iii) at most one head. The instructor begins to explain the problem, and the on-screen text clearly states the question and its parts.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins to solve the problem by first defining the sample space. On the digital whiteboard, he writes "Total = {HH, HT, TH, TT}" to list all possible outcomes of two coin tosses. He then explains that the total number of outcomes is 4. For part (i), "exactly one head," he identifies the favorable outcomes as {HT, TH}. He writes "(i) Fav outcome = {HT, TH}" and calculates the probability as P(i) = 2/4 = 1/2. For part (ii), "at least one head," he identifies the favorable outcomes as {HH, HT, TH}, writing "(ii) 1 Head OR 2 Head = {HH, HT, TH}". He calculates P(ii) = 3/4. The instructor uses a red pen to write all the text and equations on the screen, making the process clear and easy to follow.

  3. 5:00 – 8:33 05:00-08:33

    The instructor moves to part (iii), "at most one head." He defines the favorable outcomes as {HT, TH, TT}, writing "(iii) 0 Head OR 1 Head = {HT, TH, TT}". He calculates the probability as P(iii) = 3/4. He then demonstrates an alternative method for part (ii) using the complement rule. He writes "P(E') = 1 - P(E)" and identifies the event E as "at least one head." The complement E' is "no head," which corresponds to the outcome {TT}. He calculates P(E') = 1/4 and then P(E) = 1 - 1/4 = 3/4, confirming the result from the direct method. The video concludes with a final screen that says "THANKS FOR WATCHING".

The video presents a clear and structured lesson on calculating probabilities for compound events. It begins by establishing the sample space for a simple experiment (two coin tosses) and then applies the basic probability formula to three different, related events. The instructor effectively uses both direct enumeration of favorable outcomes and the complement rule, demonstrating two essential problem-solving strategies. The visual aid of the digital whiteboard allows for a step-by-step walkthrough, making the logical progression from problem statement to solution easy to follow. The lesson reinforces the fundamental concept that probability is the ratio of favorable outcomes to the total number of possible outcomes.

Loading lesson…