Here are the answers to the statements:

a) False
The probability of an event that is sure to occur is 1, not 1/2. Hence, the correct answer is false.

b) True
When three coins are thrown, there are $2^3 = 8$ possible outcomes, so $n(S) = 8$.

c) True
If the set of all possible outcomes is the event itself, the probability of that event is indeed 1.

d) True
The probability of any event lies between 0 and 1, inclusive. So the range of probability is indeed from 0 to 1.

Would you like any more details or have any questions about this?

Here are five related questions:

1. What is the probability of an impossible event?
2. How many possible outcomes are there when throwing four coins at once?
3. What is the probability of getting heads in at least one coin toss when three coins are thrown?
4. Can the probability of any event exceed 1? Why or why not?
5. What is the probability of not getting any heads when throwing two coins?

Tip: When calculating the total number of outcomes in an experiment involving coins, always use the formula $2^n$, where $n$ is the number of coins.