A number cube is rolled three times in a row. Find each probabilit 17. \( P \) (all + 's) 18. \( P \) (odd number, then odd number, then even number)
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When rolling a six-sided number cube (die), the probability of getting a '+' (considering '+' as a specific outcome like rolling a 6) on any single roll is \( \frac{1}{6} \). Therefore, the probability of rolling three '+'s in a row is \( P(all + 's) = \left(\frac{1}{6}\right)^3 = \frac{1}{216} \). For the second scenario, the probability of rolling an odd number (1, 3, or 5) is \( \frac{3}{6} = \frac{1}{2} \) and the probability of rolling an even number (2, 4, or 6) is also \( \frac{3}{6} = \frac{1}{2} \). Thus, the probability of rolling odd, then odd, then even is \( P(odd, odd, even) = \left(\frac{1}{2}\right)^2 \times \left(\frac{1}{2}\right) = \frac{1}{8} \).