For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes.
Example
For two fair coin tosses the sample space is HH, HT, TH, TT, so the probability of exactly one head is 2/4 = 1/2.
Key terms
Sample space:
The complete set of possible outcomes.
Favourable outcome:
An outcome that satisfies the event.
Equally likely:
Outcomes that have the same chance of occurring.
Questions
1. What does Sample space mean?
An outcome that satisfies the event.
The complete set of possible outcomes.
Outcomes that have the same chance of occurring.
A value selected without mathematical context.
2. Which statement correctly describes Favourable outcome?
The complete set of possible outcomes.
Outcomes that have the same chance of occurring.
An outcome that satisfies the event.
A step that removes the need to calculate.
3. Which definition matches Equally likely?
Outcomes that have the same chance of occurring.
The complete set of possible outcomes.
An outcome that satisfies the event.
A label that can be ignored when solving.
4. Which worked example belongs to theoretical probability?
An example that changes the given values before starting.
An example that gives a result without a mathematical method.
Assuming outcomes are equally likely when the design gives them different chances.
For two fair coin tosses the sample space is HH, HT, TH, TT, so the probability of exactly one head is 2/4 = 1/2.
5. Which practice approach is most reliable?
List the sample space systematically, count favourable outcomes and simplify the probability.
Assuming outcomes are equally likely when the design gives them different chances.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
6. Which action is a sensible accuracy check?
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Check that no possible outcome is missing and that probabilities for all outcomes total 1.
Change the units after calculating without using a conversion.
7. Where could theoretical probability be applied?
In a situation with no quantities or relationships.
Analyse the fairness of a dice, card, spinner or two-stage chance game.
Only in a memorised classroom example.
In place of reading the conditions of a problem.
8. A student is beginning a theoretical probability problem. What should they do?
Assuming outcomes are equally likely when the design gives them different chances.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
List the sample space systematically, count favourable outcomes and simplify the probability.
9. Which mistake is most important to avoid here?
Writing down the units supplied in the question.
Assuming outcomes are equally likely when the design gives them different chances.
Showing intermediate working.
Checking the result using the original information.
10. After calculating, which step gives the strongest evidence that the result is valid?
Check that no possible outcome is missing and that probabilities for all outcomes total 1.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
11. Which task transfers this mathematics into a meaningful context?
Copy a completed answer without its method.
List unrelated numbers from the question.
Analyse the fairness of a dice, card, spinner or two-stage chance game.
Repeat a definition without using it.
12. Why is the worked theoretical probability example valid?
It avoids the defining relationship in the topic.
For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes.
It treats every numerical operation as interchangeable.
It relies on the answer being visually complicated.
13. Which statement best connects Sample space and Favourable outcome?
Sample space and Favourable outcome are unrelated labels.
Sample space removes the need for Favourable outcome.
The meanings of Sample space and Favourable outcome can be swapped.
The complete set of possible outcomes. An outcome that satisfies the event.
14. Which response shows mathematical reasoning rather than guessing?
List the sample space systematically, count favourable outcomes and simplify the probability. Then check that no possible outcome is missing and that probabilities for all outcomes total 1.
Assuming outcomes are equally likely when the design gives them different chances.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
15. Which explanation would best justify a final answer?
The answer must be right because it was completed quickly.
The method does not need to match the quantities or conditions.
For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes. The result can be checked by this step: Check that no possible outcome is missing and that probabilities for all outcomes total 1.
A different result was ignored because it was inconvenient.
16. A result seems unreasonable. What is the best diagnostic response?
Keep the result and remove the working.
Check for this common error: Assuming outcomes are equally likely when the design gives them different chances. Then check that no possible outcome is missing and that probabilities for all outcomes total 1.
Change the original question so the result fits.
Choose a new answer without revisiting the method.
17. Which plan would produce the clearest solution for another reader?
Assuming outcomes are equally likely when the design gives them different chances.
Apply a familiar rule before identifying what the quantities represent.
Round every value at the beginning and do not check the effect.
List the sample space systematically, count favourable outcomes and simplify the probability. Show the working clearly and label the final result.
18. Which check is most closely tied to the mathematics in this topic?
Check that no possible outcome is missing and that probabilities for all outcomes total 1.
Assume the first answer is correct because a calculator produced it.
Check only that an answer has several digits.
Change the units after calculating without using a conversion.
19. Which application requires the ideas from this topic?
A task with no measurable information or decision.
A task that forbids using the stated mathematical relationship.
Analyse the fairness of a dice, card, spinner or two-stage chance game.
A task solved by copying an unrelated formula.
20. Which critique identifies a genuine flaw in a solution?
The solution states the relevant units.
Assuming outcomes are equally likely when the design gives them different chances.
The solution shows an intermediate step.
The solution checks its answer.
21. What is the strongest summary of theoretical probability?
It is a topic where units, conditions and checks never matter.
It is solved by choosing any operation that gives a whole number.
It has no connection to mathematical reasoning or real situations.
For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes.
Answer key (parent copy)
1. The complete set of possible outcomes.
2. An outcome that satisfies the event.
3. Outcomes that have the same chance of occurring.
4. For two fair coin tosses the sample space is HH, HT, TH, TT, so the probability of exactly one head is 2/4 = 1/2.
5. List the sample space systematically, count favourable outcomes and simplify the probability.
6. Check that no possible outcome is missing and that probabilities for all outcomes total 1.
7. Analyse the fairness of a dice, card, spinner or two-stage chance game.
8. List the sample space systematically, count favourable outcomes and simplify the probability.
9. Assuming outcomes are equally likely when the design gives them different chances.
10. Check that no possible outcome is missing and that probabilities for all outcomes total 1.
11. Analyse the fairness of a dice, card, spinner or two-stage chance game.
12. For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes.
13. The complete set of possible outcomes. An outcome that satisfies the event.
14. List the sample space systematically, count favourable outcomes and simplify the probability. Then check that no possible outcome is missing and that probabilities for all outcomes total 1.
15. For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes. The result can be checked by this step: Check that no possible outcome is missing and that probabilities for all outcomes total 1.
16. Check for this common error: Assuming outcomes are equally likely when the design gives them different chances. Then check that no possible outcome is missing and that probabilities for all outcomes total 1.
17. List the sample space systematically, count favourable outcomes and simplify the probability. Show the working clearly and label the final result.
18. Check that no possible outcome is missing and that probabilities for all outcomes total 1.
19. Analyse the fairness of a dice, card, spinner or two-stage chance game.
20. Assuming outcomes are equally likely when the design gives them different chances.
21. For equally likely outcomes, theoretical probability is favourable outcomes divided by total possible outcomes. A complete sample space helps avoid missing or double-counting outcomes.