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

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  1. Class 11
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Ex16.2, 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 C = (1, 4)(2, 3)(3, 2)(4, 1)(1, 3) 2, 2 3, 1 1, 2 2, 1 (1, 1) Ex16.2, 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 Ex16.2,6 (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 Ex16.2,6 (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 Ex16.2, 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 = Ex16.2, 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, 4)(2, 3)(3, 2)(4, 1)(1, 3) 2, 2 3, 1 1, 2 2, 1 (1, 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 Ex16.2, 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, 4)(2, 3)(3, 2)(4, 1)(1, 3) 2, 2 3, 1 1, 2 2, 1 (1, 1) B or C = B C = 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 , 2, 3 , 4, 1 , 2, 2 , (2, 1) Ex16.2, 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 ,} Ex16.2, 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, 4)(2, 3)(3, 2)(4, 1)(1, 3) 2, 2 3, 1 1, 2 2, 1 (1, 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) Now, 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 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) 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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