To determine which event has the highest likelihood of occurring, we need to calculate the probabilities of each event.
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Spinner lands on either purple or red (2 out of 3 possibilities) and number cube lands on 3 (1 out of 6 possibilities): \[ P(\text{Purple or Red}) = \frac{2}{3}, \quad P(3) = \frac{1}{6} \] Combined probability: \[ P(\text{Event 1}) = \frac{2}{3} \times \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \]
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Spinner lands on either green or red (2 out of 3 possibilities) and number cube lands on 6 (1 out of 6 possibilities): \[ P(\text{Green or Red}) = \frac{2}{3}, \quad P(6) = \frac{1}{6} \] Combined probability: \[ P(\text{Event 2}) = \frac{2}{3} \times \frac{1}{6} = \frac{2}{18} = \frac{1}{9} \]
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Spinner lands on red (1 out of 3 possibilities) and number cube lands on an even number (3 out of 6 possibilities): \[ P(\text{Red}) = \frac{1}{3}, \quad P(\text{Even}) = \frac{3}{6} = \frac{1}{2} \] Combined probability: \[ P(\text{Event 3}) = \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \]
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Spinner lands on red (1 out of 3 possibilities) and number cube lands on 6 (1 out of 6 possibilities): \[ P(\text{Event 4}) = \frac{1}{3} \times \frac{1}{6} = \frac{1}{18} \]
Now we can compare the probabilities:
- Event 1: \( \frac{1}{9} \)
- Event 2: \( \frac{1}{9} \)
- Event 3: \( \frac{1}{6} \)
- Event 4: \( \frac{1}{18} \)
To compare these fractions, we can convert them to have a common denominator (for example, 18):
- Event 1: \( \frac{2}{18} \)
- Event 2: \( \frac{2}{18} \)
- Event 3: \( \frac{3}{18} \)
- Event 4: \( \frac{1}{18} \)
The event with the highest probability is Event 3: The spinner lands on red, and the number cube lands on an even number, with a probability of \( \frac{1}{6} \).