A group of students were asked which club they planned to join.



ClubPercent of Students

Garden Club

0.1

Robotics Club

0.2

Technology Club

0.5

Zoology Club

0.2


Compare the probabilities of a randomly selected student joining a club and interpret the likelihood. Choose the statement that is true.

 The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden). The student will be equally likely to join the Robotics Club or Technology Club because P(Robotics) = P(Technology). The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics). The student will be more unlikely to join the Garden Club than the Robotics Club because P(Garden) < P(Robotics).

Let's compare the probabilities for each club based on the given percentages:

- **Garden Club:** 10% or 0.1
- **Robotics Club:** 20% or 0.2
- **Technology Club:** 50% or 0.5
- **Zoology Club:** 20% or 0.2

Now, let's analyze each statement:

1. **The student will be more unlikely to join the Robotics Club than the Garden Club because P(Robotics) < P(Garden).**
   - False. P(Robotics) = 0.2 and P(Garden) = 0.1. Thus, P(Robotics) > P(Garden).

2. **The student will be equally likely to join the Robotics Club or Technology Club because P(Robotics) = P(Technology).**
   - False. P(Robotics) = 0.2 and P(Technology) = 0.5. They are not equal.

3. **The student will be more likely to join the Zoology Club than the Robotics Club because P(Zoology) > P(Robotics).**
   - False. P(Zoology) = 0.2 and P(Robotics) = 0.2. They are equal, not greater.

4. **The student will be more unlikely to join the Garden Club than the Robotics Club because P(Garden) < P(Robotics).**
   - True. P(Garden) = 0.1 and P(Robotics) = 0.2. P(Garden) is less than P(Robotics), meaning it is less likely to join the Garden Club.

So, the correct statement is: **The student will be more unlikely to join the Garden Club than the Robotics Club because P(Garden) < P(Robotics).**

Would you like further details or have any questions?

Here are 8 related questions to expand on this topic:
1. What is the combined probability of a student joining either the Robotics Club or the Technology Club?
2. If a student cannot join more than one club, what is the probability of not joining the Garden Club?
3. How would the probabilities change if the Technology Club’s percentage increased to 60%?
4. What is the probability that a randomly selected student joins any club other than the Technology Club?
5. If the Zoology Club increased its percentage to 30%, how would the interpretation change?
6. What is the probability that a randomly selected student does not join the Robotics Club or the Garden Club?
7. How does the sum of all the probabilities help verify the data’s accuracy?
8. If the Garden Club doubled its percentage to 20%, how would this affect the likelihood comparisons?

**Tip:** When comparing probabilities, always ensure you accurately understand the inequalities and relationships between them to make correct interpretations.

Understand the probabilities of joining different clubs based on student choices. Analyze the likelihood of joining the Garden Club, Robotics Club, Technology Club, and Zoology Club with detailed percentages. Learn which club students are more likely to join based on probability calculations.

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