Boards Concepts Booster Class 12 Probability

1. BOARDS CONCEPTS BOOSTER PROBABILITY  Download Doubtnut Today Ques No. Question CONCEPT FOR BOARDS || Chapter PROBABILITY 1. INTRODUCTION 1 1. Introduction and definition  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 2. MATHEMATICAL OR CLASSICAL DEFINITION OF PROBABILITY 2 1. Various terms learned in earlier classes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 2. MATHEMATICAL OR CLASSICAL DEFINITION OF PROBABILITY 2. Verbal description of set and equivalent set theory notation and proof with venn diagram 3  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 2. MATHEMATICAL OR CLASSICAL DEFINITION OF PROBABILITY

2. 4 3. Probability of an event: definition  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 2. MATHEMATICAL OR CLASSICAL DEFINITION OF PROBABILITY 4. What is the probability that four 'S' comes consecutively in the word 'MISSISSIPPI` when rearranged? 5  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 3. COMPOUND AND CONDITIONAL PROBABILITY 6 1. Compound events and definition of conditional probability  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 3. COMPOUND AND CONDITIONAL PROBABILITY 2. 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? 7  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 3. COMPOUND AND CONDITIONAL PROBABILITY 8 3. Multiplication Theorems on Probability  Click to LEARN this concept/topic on Doubtnut

3. CONCEPT FOR BOARDS || Chapter PROBABILITY 3. COMPOUND AND CONDITIONAL PROBABILITY 4. A bag contains 5 white; 7 red and 8 black balls. If four balls are drawn one by one without replacement; find the probability of getting all white balls. 9  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 4. ADDITION THEOREM OF PROBABILITY 10 1. Addition Theorem Of Probability  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 4. ADDITION THEOREM OF PROBABILITY 2. A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good? 11  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 12 1. Dependent and independent events  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 2. If A and B are independent events associated with a random experiment; then

4. 13 P(A ∩ B) = P(A)P(B)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 14 3. Pairwise and mutually independent events  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 4. If A and B are independent events only associated with a random experiment; then prove that ( and B); (A and ); ( and ¯ ¯ ¯ A ¯ ¯ ¯ B ¯ ¯ ¯ A ¯ ¯ ¯ B 15 ) are also independent events.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 16 5. Independent experiments  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 6. Events A and B are such that 17 1

5. 1 P(A) = ;P(B) 2 7 = 12 B) =1 and . State whether A and B are independent? P(¯ ¯ ¯ A ∪¯ ¯ ¯ 4  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 7. A die is thrown once. If A is the event 'the number appearing is a multiply of 3` and B is the event 'the number appearing is even'. Are the events A and B independent? 18  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 8. A bag contains 5 white;7 red and 4 black balls. If four balls are drawn one by one with replacement; what is the probability that none is white? 19  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 9. A problem in mathematics is given to 3 students whose chances of solving it are 1 1 1 20 . What is the probability that the problem is solved? , , 2 3 4  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY

6. 5. INDEPENDENT EVENTS 21 10. Two balls are drawn from an urn containing 2 white; 3 red and 4 black balls one by one without replacement. What is the probability that at least one ball is red?  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 5. INDEPENDENT EVENTS 11. If then P(A1∩ A2∩ ....... are independent events associated with a random experiment; A1,A2,..... An 22 ∩ An) = P(A1)P(A2)...... .P(An)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 6. PROBLEMS ON TOTAL PROBABILITY THEOREM 23 1. Law of total probability  Click to LEARN this concept/topic on Doubtnut

7. CONCEPT FOR BOARDS || Chapter PROBABILITY 6. PROBLEMS ON TOTAL PROBABILITY THEOREM 2. A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag; one ball is drawn. Find the probability that the ball drawn is red. 24  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 7. BAYES THEOREM 25 1. Bayes' Theorem: proof and meaning  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 7. BAYES THEOREM 2. A card from a pack of 52 cards is lost. From the remaining cards of the pack; two cards are drawn and are found to be hearts. Find the probability of the missing card to be a heart. 26  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 8. PROBLEMS ON BAYES'S THEOREM 27 1. Probability calculation by graph  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 9. BERNOULLI TRIALS AND BINOMIAL DISTRIBUTION

8. 28 1. Type of random variables  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 9. BERNOULLI TRIALS AND BINOMIAL DISTRIBUTION 29 2. Discrete random variable  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 9. BERNOULLI TRIALS AND BINOMIAL DISTRIBUTION 30 3. Probability distribution and graphical representation  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 10. PROPERTIES OF CONDITIONAL PROBABILITY 1. Let A and B be two events associated with sample space S; then 31 A 0 ≤ P( ) ≤ 1 B  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 10. PROPERTIES OF CONDITIONAL PROBABILITY 2. If A is an event associated with the sample space S of an random experiment; then 32

9. A S P( ) = P( ) A A = 1  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 10. PROPERTIES OF CONDITIONAL PROBABILITY 3. Let A and B be two events associated with a random experiment and S be the sample space. If C is an event such that P(C) ≠ 0 then AUB P( ) C A = P( ) C 33 B + P( ) C A ∩ B − P( ) C  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter PROBABILITY 10. PROPERTIES OF CONDITIONAL PROBABILITY 4. If A and B are two events associated with a random experiment; then ¯ ¯ ¯ A P( ) = 1 34 B A − P( ) B  Click to LEARN this concept/topic on Doubtnut  Download Doubtnut to Ask Any Math Question By just a click  Get A Video Solution For Free in Seconds  Doubtnut Has More Than 1 Lakh Video Solutions  Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage (G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana, VidyaMandir  Download Doubtnut Today