A coin is tossed three times, consider the following events. A : No head appears, B: Exactly one head appears and C: Atleast two appear. Do they form a set of mutually exclusive and exhaustive events?

Explanation

The sample space of the experiment is,
S ={HHH, HHT, HTH, THH, ITT, TTH, THT, HTT}
Here, A = {m},B = {TTH, THT, HTT} C = {HHT, HTH, THH, HHH}
Now, A ∪ B ∪ C = {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH}
⇒ A ∪ B ∪ C = S
⇒ A, B and C are exhaustive events.
Also A∩B = ϕ,A∩C = ϕ and B∩C = ϕ
⇒ A, B and C are mutually exclusive.
Hence A, B and C are mutually exclusive and exhaustive events.