Question

Question 2 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 U B, A ∩ B, B U C, E ∩ F, D ∩ E, A - C, D - E, E ∩ F', F'

Class X1 - Maths -Probability Page 393

Answer 1

when A die is thrown then , total number of possible outcomes is 6 .
S ( sample space ) = {1,2,3,4,5,6}

(i) A : a number less than 7
we observed that 1 to 6 number are include in die hence, A = { 1, 2, 3, 4, 5, 6 }

(ii) B : a number greater than 7
only 1 to 6 number is appear in die so,
B = Φ

(iii) C : a multiple of 3
in die 3 , 6 are multiple of 3
so, C = { 3, 6 }

(iv) D : a number less than 4
there are three number include in die which are less than 4 .
D = { 1, 2, 3 }

(v) E : an even number greater than 4
there is only one number which is greater than 4 and it is an even number .
E = { 6}

(vi) F : a number not less than 3 or we can say that a number greater than or equal to 3
e.g., F = {3,4,5,6}

now,

A U B = {1,2,3,4,5,6} U Φ = {1,2,34,5,6}
A ∩ B = {1,2,3,4,5,6} ∩ Φ = Φ
B U C = Φ U {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}
E ∩ F' = E ∩( S - F) = E ∩ {1,2,3,4,5,6}-{3,4,5,6}
{6} ∩ {1,2} = Φ
F' = {1,2}