Question

In each of the following experiments, write the sample space S, number of sample points n(S), event A,B,C and n(A), n(B), n(C), also find complementary events, mutually exclusive events:

A coin is tossed three times.A is the event that head appears once, B is the event that head appeared at the most twice, C is the event that tail does not appear.

Answer 1

Given:
A coin is tossed three times.
Thus, the sample space is {HHH, THH, HTH, HHT, THT, TTH, HTT, TTT}.
∴ n(S) = 8
Now,
A is the event that the head appears once.
∴ A = {THT, TTH, HTT}
Or,
n(A) = 3
B is the event that the head appears at most twice.
∴ B = {THH, HTH, HHT, THT, TTH, HTT, TTT}
Or,
n(B) = 7
C is the event that the tail does not appear.
∴ C = {HHH}
Or,
n(C) = 1
Here,
B $\cap$ C = $\varnothing$ and B $\cup$ C = S
Events B and C are mutually exclusive and complementary.