A coin is tossed three times consider the following event A: No head appears, B: Exactly one head appears and C: At least two heads appears do they form a set of mutually exclusive and exhaustive events.

Question

A coin is tossed three times consider the
following event A: No head appears, B: Exactly one head appears and
C: At least two heads appears do they form a set of mutually
exclusive and exhaustive events

Gursheen kaur. · Accepted Answer

The possibilities are:
H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T
The total outcomes=8
a) 
No head appears

No of fav outcomes(T T T)=1
Probability = 1/8

b) 
Exactly one head appears

No of fav outcomes(H T T),(T H
T),(T T H)=3
Probability = 3/8

c) 
At least two heads appears

No of fav outcomes(H H T),(H T
H),(T H H)=3
Probability = 3/8

Yes, they form a set of mutually exclusive
and exhaustive events