Check sibling questions

Ex 16.2, 6 - Two dice are thrown. The events A, B, C are

Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 2

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 3

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 4

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 5

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 6

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 7

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 8

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 9

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Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 10

Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 11
Ex 16.2, 6 - Chapter 16 Class 11 Probability - Part 12

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Transcript

Ex 16.2, 6 Two dice are thrown. The events A, B and C are as follows: A: getting an even number on the first die. B: getting an odd number on the first die. C: getting the sum of the numbers on the dice ≤ 5 Describe the events If 2 dies are thrown then possible outcomes are 1, 2, 3, 4, 5, 6 on both dies S = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @"(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @"(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} A: getting an even number on the first die A = {█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} B: getting an odd number on the first die B = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @" (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @" (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) " )} C: getting the sum of the numbers on the dice ≤ 5 "(1, 1), (1, 2), (1, 3), (1, 4), " "(2, 1), (2, 2), (2, 3)," Ex 16.2, 6 A’ S = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @"(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @"(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} A = {█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} A’ = S – A A’ = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @" (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), " )} = Getting odd number on the first die = B Ex 16.2, 6 (ii) not B S = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @" (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), " @"(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @" (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}" )} B = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @" (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @" (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) " )} not B = S – B not B = {█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} = Getting even number of the first die = A Ex 16.2, 6 (iii) A or B A = {█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} B = {█(█((1, 1),(1, 2),(1, 3),(1, 4),(1, 5),(1, 6),@(3, 1),(3, 2),(3, 3)," " (3, 4),(3, 5),(3, 6) )@(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6) )} A or B = A ∪ B = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @" (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), " @"(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @" (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} = S Ex 16.2, 6 (iv) A and B A ={█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} B = {█(█((1, 1),(1, 2),(1, 3),(1, 4),(1, 5),(1, 6),@(3, 1),(3, 2),(3, 3)," " (3, 4),(3, 5),(3, 6) )@(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6) )} A and B = A ∩ B = 𝛟 Ex 16.2, 6 (v) A but not C A = {█("(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), " @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} C = {█((1, 1), (1, 2), (1, 3), (1, 4),@(2, 1), (2, 2), (2, 3),@(3, 1), (3, 2), (4, 1))} A but not C = A – C = {█(█((2, 4),(2, 5),(2, 6),@(4, 2),(4, 3),(4, 4),(4, 5),(4, 6)"," )@█((6, 1),(6, 2),(6, 3),(6, 4),(6, 5),(6 6) ))} Ex 16.2, 6 (vi) B or C B = {█(█((1, 1),(1, 2),(1, 3),(1, 4),(1, 5),(1, 6),@(3, 1),(3, 2),(3, 3)," " (3, 4),(3, 5),(3, 6) )@(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6) ),} C = {█((1, 1), (1, 2), (1, 3), (1, 4),@(2, 1), (2, 2), (2, 3),@(3, 1), (3, 2), (4, 1))} B or C = B ∪ C = {█(█((1, 1),(1, 2),(1, 3),(1, 4),(1, 5),(1, 6),@(2, 1), (2, 2), (2, 3),@(3, 1),(3, 2),(3, 3)," " (3, 4),(3, 5),(3, 6),@(4, 1),)@(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6),)} Ex 16.2, 6 (vii) B and C B = {█((1, 1),(1, 2),(1, 3),(1, 4),(1, 5),(1, 6)", " @█((3, 1),(3, 2),(3, 3), (3, 4),(3, 5),(3, 6)@(5, 1),(5, 2),(5, 3),(5, 4),(5, 5),(5, 6) ))} C = {█((1, 1), (1, 2), (1, 3), (1, 4),@(2, 1), (2, 2), (2, 3),@(3, 1), (3, 2), (4, 1))} B and C = B ∩ C = {(1, 1),(1, 2),(1, 3),(1, 4), (3, 1),(3, 2),} Ex 16.2, 6 (viii) A ∩ B’ ∩ C’ We know A & B’ (calculated in part(ii)) Finding C’ S = {█("(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)," @"(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)," @"(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @"(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} C = {█((1, 1), (1, 2), (1, 3), (1, 4),@(2, 1), (2, 2), (2, 3),@(3, 1), (3, 2), (4, 1))} C’ = S – C = {█("(1, 5), (1, 6)," @"(2, 4), (2, 5), (2, 6)," @ "(3, 3), (3, 4), (3, 5), (3, 6)," @"(4, 2), (4, 3), (4, 4), (4, 5), (4, 6)," @"(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)," @"(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)" )} Also, A = {█((2, 1),(2, 2),(2, 3),(2, 4),(2, 5),(2, 6),@█((4, 1),(4, 2),(4, 3),(4, 4),(4, 5),(4, 6),@(6, 1),(6, 2),(6, 3),(6, 4),(6, 5),(6, 6) ))} B’ = {█((2, 1),(2, 2),(2, 3),(2, 4),(2, 5),(2, 6),@█((4, 1),(4, 2),(4, 3),(4, 4),(4, 5),(4, 6),@(6, 1),(6, 2),(6, 3),(6, 4),(6, 5),(6, 6) ))} Thus, A ∩ B’ ∩ C’ = {█((2, 4),(2, 5),(2, 6)"," @" " (4, 2),(4, 3),(4, 4),(4, 5),(4, 6),@(6, 1),(6, 2),(6, 3),(6, 4),(6, 5),(6 6) )}

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.