Conditional Probability Class 12 | Probability Chapter 13 Part 1 | NCERT | By Faiz Sir скачать в хорошем качестве

Conditional Probability Class 12 | Probability Chapter 13 Part 1 | NCERT | By Faiz Sir

PROBABILITY – Class 12 | Chapter 13 | Conditional Probability | NCERT | CBSE | By Faiz Sir Is video mein Class 12 Maths Chapter 13 – Probability (Part 1) ka introduction aur Conditional Probability ko properties, formulas, solved examples aur important questions ke saath detail mein samjhaya gaya hai. Aap seekhenge: ✔ Definition of Conditional Probability ✔ Properties of Conditional Probability ✔ Solved NCERT Examples ✔ Important Board Exam Questions ✔ Real-life Probability Problems ✔ Exam-oriented MCQs and Practice Questions 📌 Covered Topics: Conditional Probability Formula Properties of Conditional Probability Bayes Concept Basics Probability of Dependent Events Dice, Cards, Coin & Real-Life Examples CBSE Board Important Questions 🎯 Perfect for CBSE Class 12 Board Exams, CUET, JEE Basics & Quick Revision 📢 Subscribe to Infinix Classes Maths by Faiz Sir for complete Class 11 & 12 Maths preparation. Probability Class 12, Conditional Probability Class 12, Probability Chapter 13 NCERT, Class 12 Maths Probability, Conditional Probability NCERT, CBSE Probability, Probability Part 1 Class 12, Dependent Events Probability, Bayes Theorem Basics, Dice Probability Questions, Coin Probability Class 12, NCERT Maths Class 12, Infinix Classes Maths, Faiz Sir Maths, Probability Examples Class 12, Probability Important Questions, Probability Hindi, Probability English, कक्षा 12 प्रायिकता, सशर्त प्रायिकता, Class 12 Maths Board Exam, Probability One Shot #ProbabilityClass12 #ConditionalProbability #Class12Maths #Chapter13Probability #NCERTMaths #CBSE2025 #BoardExamPreparation #InfinixClasses #FaizSirMaths #MathsByFaizSir #ProbabilityPart1 #ImportantQuestions #ExamReady #CUETPrep #JEEBasics PROBABILITY | Class - 12 | Chapter – 13 | NCERT | By : FAIZ SIR Conditional Probability: Definition 1: If E and F are two events associated with the same sample space of a random experiment, the conditional probability of the event E given that F has occurred, i.e. P (E|F) is given by Properties of conditional probability: Let E and F be events of a sample space S of an experiment, then we have Property 1: P(S|F) = P(F|F) = 1 Property 2: If A and B are any two events of a sample space S and F is an event of S such that P(F) ≠ 0, then P((A ∪ B)|F) = P(A|F) + P(B|F) – P((A ∩ B)|F) Property 3: P(E′|F) = 1 − P(E|F) Example: If P(A) = 7/13, P(B) = 9/13 and P(A ∩ B) = 4/13, evaluate P(A|B). Example: A family has two children. What is the probability that both the children are boys given that at least one of them is a boy ? Example: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number? Example: In a school, there are 1000 students, out of which 430 are girls. It is known that out of 430, 10% of the girls study in class XII. What is the probability that a student chosen randomly studies in Class XII given that the chosen student is a girl? Example: A die is thrown three times. Events A and B are defined as below: A : 4 on the third throw B : 6 on the first and 5 on the second throw Find the probability of A given that B has already occurred. Example: A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once? Example: Consider the experiment of tossing a coin. If the coin shows head, toss it again but if it shows tail, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 4’ given that ‘there is at least one tail’. Q) Determine P(E|F): Mother, father and son line up at random for a family picture E : son on one end, F : father in middle Q) An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question? Q) A fair die is rolled. Consider events E = {1,3,5}, F = {2,3} and G = {2,3,4,5} Find (i) P(E|F) and P(F|E) (ii) P(E|G) and P(G|E) (iii) P((E ∪ F)|G) and P((E ∩ F)|G) Q) If P(A) = 1/2 , P(B) = 0, then P(A|B) is (A) 0 (B) 1/2 (C) not defined (D) 1 Q) If A and B are events such that P(A|B) = P(B|A), then (A) A ⊂ B but A ≠ B (B) A = B (C) A ∩ B = φ (D) P(A) = P(B)