Answer:

We want to count the total number of heads obtained from those 4 tosses. ZZ is the random variable representing the number of heads that occur. We want to find the all possible values of ZZ.

Observe that, any one of the following cases may happen:

All the four outcomes are 'Tail'. So number of heads is 0. Hence, Z=0Z=0 in this case.

Any 3 of the 4 outcomes are 'Tail' and the remaining one is a 'Head' Hence, Z=1Z=1 in this case.

Any 2 of the 4 outcomes are 'Tail' and the remaining two are 'Head' Hence, Z=2Z=2 in this case.

Any 1 of the 4 outcomes is 'Tail' and the remaining three are 'Head' Hence, Z=3Z=3 in this case.

All the four outcomes are 'Head'. So number of heads is 4. Hence, Z=4Z=4 in this case.

Note that, the 5 cases listed above explores all possible outcomes. Hence, the random variable ZZ takes any one value from \{0,1,2,3,4\}{0,1,2,3,4}.