NCERT Class XI Mathematics - Probability - Solutions
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Question : 18
Total: 54
A die is thrown. Describe the following events:
(i) A : a number less than 7
(ii) B : a number greater than 7
(iii) C : a multiple of 3
(iv) D : a number less than 4
(v) E : an even number greater than 4
(vi) F : a number not less than 3
Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F′, F′.
(i) A : a number less than 7
(ii) B : a number greater than 7
(iii) C : a multiple of 3
(iv) D : a number less than 4
(v) E : an even number greater than 4
(vi) F : a number not less than 3
Also find A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A – C, D – E, E ∩ F′, F′.
Solution:
An experiment consists of rolling a die.
S = {1, 2, 3, 4, 5, 6}
(i) A : a number less than 7 = {1, 2, 3, 4, 5, 6}
(ii) B : a number greater than 7 = ϕ
(iii) C : a multiple of 3 = {3, 6}
(iv) D : a number less than 4 = {1, 2, 3}
(v) E : an even number greater than 4 = {6}
(vi) F : a number not less than 3 = {3, 4, 5, 6}
\ A ∪ B = {1, 2, 3, 4, 5, 6} ∪ ϕ = {1, 2, 3, 4, 5, 6}
A ∩ B = {1, 2, 3, 4, 5, 6} ∩ ϕ = ϕ
B ∪ C = f ∪ {3, 6} = {3, 6}
E ∩ F = {6} ∩ {3, 4, 5, 6} = {6}
D ∩ E = {1, 2, 3} ∩ {6} = ϕ
A – C = {1, 2, 3, 4, 5, 6} – {3, 6} = {1, 2, 4, 5}
D – E = {1, 2, 3} – {6} = {1, 2, 3}
F′ = {1, 2, 3, 4, 5, 6} – {3, 4, 5, 6} = {1, 2}
E ∩ F′ = {6} ∩ {1, 2} = ϕ
S = {1, 2, 3, 4, 5, 6}
(i) A : a number less than 7 = {1, 2, 3, 4, 5, 6}
(ii) B : a number greater than 7 = ϕ
(iii) C : a multiple of 3 = {3, 6}
(iv) D : a number less than 4 = {1, 2, 3}
(v) E : an even number greater than 4 = {6}
(vi) F : a number not less than 3 = {3, 4, 5, 6}
\ A ∪ B = {1, 2, 3, 4, 5, 6} ∪ ϕ = {1, 2, 3, 4, 5, 6}
A ∩ B = {1, 2, 3, 4, 5, 6} ∩ ϕ = ϕ
B ∪ C = f ∪ {3, 6} = {3, 6}
E ∩ F = {6} ∩ {3, 4, 5, 6} = {6}
D ∩ E = {1, 2, 3} ∩ {6} = ϕ
A – C = {1, 2, 3, 4, 5, 6} – {3, 6} = {1, 2, 4, 5}
D – E = {1, 2, 3} – {6} = {1, 2, 3}
F′ = {1, 2, 3, 4, 5, 6} – {3, 4, 5, 6} = {1, 2}
E ∩ F′ = {6} ∩ {1, 2} = ϕ
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