Given: A dice is thrown once.
Let us find the given events, and also find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and
bar F.
S = {1, 2, 3, 4, 5, 6}
According to the subparts of the question, we have certain events as:
(i) A = getting a number below 7
So, the sample spaces for A are:
A = {1, 2, 3, 4, 5, 6}
(ii) B = Getting a number greater than 7
So, the sample spaces for B are:
B = {Փ}
(iii) C = Getting multiple of 3
So, the Sample space of C is
C = {3, 6}
(iv) D = Getting a number less than 4
So, the sample space for D is
D = {1, 2, 3}
(v) E = Getting an even number greater than 4.
So, the sample space for E is
E = {6}
(vi) F = Getting a number not less than 3.
So, the sample space for F is
F = {3, 4, 5, 6}
Now,
A = {1, 2, 3, 4, 5, 6} and B = {Փ}
A ⋃ B = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3, 4, 5, 6} and B = {Փ}
A ⋂ B = {Փ}
B = {Փ} and C = {3, 6}
B ⋂ C = {Փ}
F = {3, 4, 5, 6} and E = {6}
E ⋂ F = {6}
E = {6} and D = {1, 2, 3}
D ⋂ F = {3}
