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 = ϕ 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﷯} ≠ 𝜙 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 ≠ ϕ 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’ = 𝝓 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 ≠ 𝜙 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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