Pregunta
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A number cube is rolled three times in a row. Find each probabilit
17. (all + 's)
18. (odd number, then odd number, then even number)

Ask by Logan Simmons. in the United States
Mar 15,2025

Solución de inteligencia artificial de Upstudy

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The probability of all + 's is or about 0.0046. The probability of rolling an odd number, then another odd number, then an even number is or about 0.125.

Solución

To find the probabilities of the given events, we need to consider the outcomes of rolling a number cube three times in a row.
  1. Probability of all + 's:
    • The probability of rolling a + on a number cube is 1/6.
    • Since the cube is rolled three times, the probability of all + 's is .
  2. Probability of odd number, then odd number, then even number:
    • The probability of rolling an odd number on a number cube is 3/6 = 1/2.
    • The probability of rolling an even number on a number cube is 3/6 = 1/2.
    • Since the cube is rolled three times, the probability of odd number, then odd number, then even number is .
Let’s calculate these probabilities.
Calculate the value by following steps:
  • step0: Calculate:
  • step1: Use the properties of exponents:
  • step2: Evaluate the power:
  • step3: Evaluate the power:
  1. The probability of all + 's is or approximately 0.0046.
  2. The probability of odd number, then odd number, then even number is or approximately 0.125.

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Bonus Knowledge

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 . Therefore, the probability of rolling three '+'s in a row is .
For the second scenario, the probability of rolling an odd number (1, 3, or 5) is and the probability of rolling an even number (2, 4, or 6) is also . Thus, the probability of rolling odd, then odd, then even is .

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