To determine the probability of rolling an odd number on a standard number cube (which has faces numbered 1 through 6), we first need to identify the odd numbers on the cube. The odd numbers are 1, 3, and 5.
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Calculate the number of odd numbers: There are 3 odd numbers (1, 3, 5) out of a total of 6 numbers on the cube.
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Calculate the probability of rolling an odd number: \[ P(\text{odd number}) = \frac{\text{Number of odd outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]
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Calculate the probability of rolling an odd number three times in a row: Since the rolls are independent, we can multiply the probabilities: \[ P(\text{odd number three times}) = P(\text{odd number}) \times P(\text{odd number}) \times P(\text{odd number}) = \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right) = \frac{1}{8} \]
Thus, the probability of rolling an odd number three times in a row is 1/8.
The correct response is: 1/8
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