Three coins are tossed once. Let A denote the event ‘three heads show’, B denote the event “two heads and one tail show”, C denote the event ‘three tails show and D denote event ‘a head shows on the first coin’, which events are: (i) multually exclusive? (ii) simple? (iii) compound?
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.