Ex 16.2, 7 - Refer to question 6 above, State true or false - Mutually Exculsive and Exhaustive Events

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) A and B are mutually exclusive From 16.2 ,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 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 B = Since no common element in A & B So, A & B are mutually exclusive True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (ii) A and B are mutually exclusive and exhaustive From 16.2 ,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 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 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 Since A B = S They are exhaustive events Also as per (i), they are mutually exclusive Hence they are mutually exclusive and exhaustive True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (iii) A = B A = getting even number on the first 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 odd no on the first die = 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 B = getting even number on the first die = 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 Hence A = B True. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (iv) A and C are mutually exclusive 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 C = { 3, 6 , 4, 5 , 5, 4 , 6, 3 , 6, 6 } Since there is common elements in A and C , So A & C are not mutually exclusive False. Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (v) A and B are mutually exclusive 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 A 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 = A Since A B = A Hence there is common element between A & B Hence A and B is not mutually exclusive Hence, false Ex16.2, 7 Refer to question 6 above, State true or false: (give reason for your answer) (vi) A, B , C are mutually exclusive and exhaustive. A = getting an even number on the first die A = getting an odd number on the first die 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 B = getting an odd number on the first die B = getting an even number on the first die 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 = (1,1),(1,2),(1,3),(1,4),(2,1), (2,2),(2,3),(3,1),(3,2),(4,1) A B = Hence there is no common element in A and B A & B are mutually exclusive B C = { 2, 1 , 2, 2 , 2, 3 , 4, 1 } Hence there is common element between B and C Since B C Hence B and C are not mutually exclusive Since B & C are not mutually exclusive A, B , C are not mutually exclusive and exhaustive A, B , C are not mutually exclusive and exhaustive Hence, false

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.