In a game using dice, one die is thrown and turns up a 6. What is the probability of getting a 6 on the throw of the other die? 23) 1 A) 3 C) B) 6 D) -IN -

A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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**Question 23: Probability in Dice Games**

In a game using dice, one die is thrown and turns up a 6. What is the probability of getting a 6 on the throw of the other die?

A) \( \frac{1}{3} \)

B) \( \frac{1}{6} \)

C) \( \frac{1}{2} \)

D) \( \frac{1}{4} \)

---

**Explanation:**

This question tests understanding of basic probability with a six-sided die. Each face of a die has an equal chance of landing face up, so if we need to calculate the probability of rolling a specific number (in this case, a 6), it is calculated as follows:

- There is 1 desired outcome (rolling a 6).
- There are 6 possible outcomes (1, 2, 3, 4, 5, 6).

The probability \( P \) of rolling a 6 on a single throw is given by:

\[ P(\text{rolling a 6}) = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} = \frac{1}{6} \]

Thus, the correct answer is B) \( \frac{1}{6} \).
Transcribed Image Text:**Question 23: Probability in Dice Games** In a game using dice, one die is thrown and turns up a 6. What is the probability of getting a 6 on the throw of the other die? A) \( \frac{1}{3} \) B) \( \frac{1}{6} \) C) \( \frac{1}{2} \) D) \( \frac{1}{4} \) --- **Explanation:** This question tests understanding of basic probability with a six-sided die. Each face of a die has an equal chance of landing face up, so if we need to calculate the probability of rolling a specific number (in this case, a 6), it is calculated as follows: - There is 1 desired outcome (rolling a 6). - There are 6 possible outcomes (1, 2, 3, 4, 5, 6). The probability \( P \) of rolling a 6 on a single throw is given by: \[ P(\text{rolling a 6}) = \frac{\text{number of desired outcomes}}{\text{number of possible outcomes}} = \frac{1}{6} \] Thus, the correct answer is B) \( \frac{1}{6} \).
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