Question

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

Answer 1

@oldrin.bataku

Answer 2

Consider the possible results of three coin flips (i.e. the state space):

TTT, TTH, THT, THH, HTT, HTH, HHT, HHH

Let's classify them by event. First, 'no head appears' -- clearly only TTT satisfies this. So now we're left with:

TTH, THT, THH, HTT, HTH, HHT, HHH

Moving on, 'exactly one head appears'. We can see that TTH, THT, and HTT all fit this category, leaving us now with only:

THH, HTH, HHT, HHH

Now, we consider 'at least two heads appear' -- and that takes care of all those left over. There was no overlap between categories (which is only logical) and thus these events are indeed mutually exclusive. Further, we took care of every possibility in our state space for coin flip sequences, so this classification is indeed exhaustive.

Answer 3

Thank you sir