(i) A : a number less than 7.
(ii) B : a number greater than 7.
(iii) C : an multiple of 3.
(iv) D : a number less-than 4.
(v) E : an even number greater than 4.
(vi) F : a number is not less than 3.
Also, find, A ∪ B, A ∩ B, B ∪ C, E ∩ F, D ∩ E, A - C, D - E, F', E ∩ F'
Three coins are tossed. The sample space is:
Event A: three heads show. A = {HHH}
Event B: two heads and one tail shows. B = {HHT, HTH, THH}
Event C: three tails show. C= {TTT}
Event D: a head shows on the first coin. D = {HHH, HHT, HTH, HTT}
(i)
∴ A and B are mutually exclusive.
∴ A and C are mutually exclusive.
∴ A and D are not mutally exclusive
∴ B and C are mutually exclusive.
∴ B and D are not mutually exclusive.
∴ C and D are mutually exclusive.
(ii) A = {HHH} n (A) = 1
∴ A is a simple event.
C = {TTT} n(C) = 1
∴ C is a simple event.
(iii) B = {HHT, HTH, THH} n(B) = 3 > 1
∴ B is a compound event.
D = {HHH, HHT, HTH, HTT} n(D) = 4 > 1
∴ D is a compound event.