To determine which table represents vanilla as an event that is "likely," we need to look at the number of students who prefer vanilla compared to the total number of students. An event is "likely" if its probability is greater than 0.5, meaning that more than half of the total students prefer vanilla.

Let's calculate the total number of students and the fraction of students who prefer vanilla for each option:

1. Option A:

   • Total number of students = $6 + 8 + 6 = 20$
   • Students who prefer vanilla = 8
   • Probability of vanilla = $\frac{8}{20} = 0.4$

2. Option B:

   • Total number of students = $2 + 17 + 1 = 20$
   • Students who prefer vanilla = 17
   • Probability of vanilla = $\frac{17}{20} = 0.85$

3. Option C:

   • Total number of students = $10 + 10 + 0 = 20$
   • Students who prefer vanilla = 10
   • Probability of vanilla = $\frac{10}{20} = 0.5$

4. Option D:

   • Total number of students = $12 + 2 + 6 = 20$
   • Students who prefer vanilla = 2
   • Probability of vanilla = $\frac{2}{20} = 0.1$

Now, let's determine which of these probabilities makes vanilla a "likely" event (greater than 0.5).

• Option A: 0.4 (Not likely)
• Option B: 0.85 (Likely)
• Option C: 0.5 (Not likely, since it's exactly 0.5)
• Option D: 0.1 (Not likely)

Conclusion: The correct answer is Option B. This is the table where vanilla is the most likely choice, with 85% (0.85 probability) of the students preferring vanilla.

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Would you like more details or have any questions? Here are some related questions:

1. How do you calculate the probability of an event?
2. What does it mean for an event to be "likely" in probability?
3. How can probability be used to make decisions?
4. How do you interpret probability values in real-world scenarios?
5. What are some examples of likely and unlikely events in everyday life?

Tip: When comparing probabilities, remember that a probability above 0.5 indicates that the event is more likely to happen than not.