To find the probability of both rolling a 6 on a six-sided number cube and spinning a vowel on a spinner with 5 equal sections labeled A through E, we need to break it down into two parts.
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Probability of rolling a 6: A six-sided number cube has numbers 1 through 6. The probability of rolling a 6 is: \[ P(\text{Rolling a 6}) = \frac{1}{6} \]
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Probability of spinning a vowel: The sections on the spinner are A, B, C, D, and E. The vowels among these letters are A and E. Therefore, the probability of spinning a vowel is: \[ P(\text{Spinning a vowel}) = \frac{2 \text{ vowels}}{5 \text{ sections}} = \frac{2}{5} \]
Next, to find the combined probability that both events occur (rolling a 6 and spinning a vowel), we multiply the two probabilities together: \[ P(\text{Rolling a 6 and spinning a vowel}) = P(\text{Rolling a 6}) \times P(\text{Spinning a vowel}) = \frac{1}{6} \times \frac{2}{5} = \frac{2}{30} = \frac{1}{15} \]
Thus, the probability of rolling a 6 and spinning a vowel is: \[ \frac{1}{15} \]
The correct response is: 1 over 15