Ex 14.1

Chapter 14 Class 11 Probability
Serial order wise

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### Transcript

Ex16.2, 3 An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events: A: the sum is greater than 8, B: 2 occurs on either die C: The sum is at least 7 and a multiple of 3. Which pairs of these events are mutually exclusive? Sample space when two dies are thrown 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 : The sum is greater than 8 Possible sum is greater than is 9, 10, 11, & 12 A = (3,6),(4,5),(5,4),(6,3),(4,6),﷮(5,5),(6,4),(5,6),(6,5),(6,6)﷯﷯ B : 2 occur on either die i.e. 2 occur either on first die or second die or both B = 2, 1﷯, 2, 2﷯, 2, 3﷯, 2, 4﷯, 2, 5﷯, 2, 6﷯,﷮ 1, 2﷯, 3, 2﷯, 4, 2﷯, 5, 2﷯, 6, 2﷯﷯﷯ C : The sum is at least 7 & multiple of 3 So, sum can be 9 or 12 C = { 3, 6﷯, 4, 5﷯, 5, 4﷯, 6, 3﷯, 6, 6﷯} If 2 elements are Mutually exclusive , then there should not be any common element (i) A ∩ B = ϕ Since no common element in A & B So, A & B are mutually exclusive (ii) B ∩ C = 𝜙 Since no common element in B & C So A & C are mutually exclusive (iii) 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

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.