Question

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

(i) Two coins are tossed, A is the event of getting at most one head, B is the event getting both heads, C is the event of getting same face on both the coins.

Answer 1

Given:
Two coins are tossed.
The sample space is {HH, TH, HT, TT}.
∴ n(S) = 4
Now,
A is the event of getting at most one head.
∴ A = {TH, HT, TT}
Or,
n(A) = 3
B is the event of getting both heads.
∴ B = {HH}
Or,
n(B) = 1
C is the event of getting the same face on both the coins.
∴ C = {HH, TT}
Or,
n(C) = 2
Here,
A $\cap$ B = $\varnothing$ and A $\cup$ B = S
Thus, we can say that events A and B are mutually exclusive and complementary.