To determine which event has the highest likelihood of occurring, let's analyze the probabilities for each option.
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The spinner lands on either green or red, and the number cube lands on 6.
- Probability of the spinner landing on green or red: \( \frac{2}{3} \) (2 favorable outcomes: green, red)
- Probability of the number cube landing on 6: \( \frac{1}{6} \)
- Combined probability: \( \frac{2}{3} \times \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \)
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The spinner lands on red, and the number cube lands on an even number.
- Probability of the spinner landing on red: \( \frac{1}{3} \)
- Probability of the number cube landing on an even number (2, 4, or 6): \( \frac{3}{6} = \frac{1}{2} \)
- Combined probability: \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \)
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The spinner lands on red, and the number cube lands on 6.
- Probability of the spinner landing on red: \( \frac{1}{3} \)
- Probability of the number cube landing on 6: \( \frac{1}{6} \)
- Combined probability: \( \frac{1}{3} \times \frac{1}{6} = \frac{1}{18} \)
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The spinner lands on either purple or red, and the number cube lands on 3.
- Probability of the spinner landing on purple or red: \( \frac{2}{3} \) (2 favorable outcomes: purple, red)
- Probability of the number cube landing on 3: \( \frac{1}{6} \)
- Combined probability: \( \frac{2}{3} \times \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \)
Now let's summarize the combined probabilities:
- Option 1: \( \frac{1}{9} \)
- Option 2: \( \frac{1}{6} \)
- Option 3: \( \frac{1}{18} \)
- Option 4: \( \frac{1}{9} \)
The event with the highest probability is Option 2: "The spinner lands on red, and the number cube lands on an even number" with a probability of \( \frac{1}{6} \).