1) Write true if the statement is correct and false if it is not.
a) The probability of an event that is sure to occur is 1
2
.
b) If three coins are thrown at a time, then n(S) = 8
c) If the set of all possible outcomes is an event, the probability of an event
is 1.
d) The range of the values of the probability of an event is between 0 and
1.


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.

1) Write true if the statement is correct and false if it is not.
a) The probability of an event that is sure to occur is 1/2.
b) If three coins are thrown at a time, then n(S) = 8.
c) If the set of all possible outcomes is an event, the probability of an event is 1.
d) The range of the values of the probability of an event is between 0 and 1.

Explore the probability of events occurring with examples like tossing coins and understanding the range of probability values. This solution covers key concepts in probability, such as sample space, event outcomes, and theorems, with problems suitable for students in Grades 6-8.

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