Question

A die was thrown \( n \) times until the lowest number on the die appeared. If the mean is \( \frac{n}{g} \), then what is the value of \( n \)?

• A. \( 2 \)
• B. \( 3 \)
• C. \( 4 \)
• D. \( 5 \)

Hint:

When dealing with dice problems, consider the probabilities of rolling the lowest numbers and use those to form equations.

Answer 1

The Correct Option is B

We are given that a die is thrown \( n \) times until the lowest number appears. The mean is given by \( \frac{n}{g} \), where \( g \) represents the lowest number on the die. Let's break down the solution:
Step 1: Understand the situation - A die has six faces, numbered from 1 to 6. - The die is thrown \( n \) times, and we are interested in the lowest number appearing on any of those throws. - The formula for the mean is \( \frac{n}{g} \), where \( n \) is the number of throws, and \( g \) is the lowest number on the die.
Step 2: Analyze the outcome - The lowest number on a die can be between 1 and 6. - The mean is based on the number of throws and the lowest number seen on the die during those throws.
Step 3: Solve for \( n \) - To find the value of \( n \), we use the formula \( \frac{n}{g} \). Since the lowest number \( g \) is most commonly 1 (assuming uniform distribution of outcomes), we can substitute \( g = 1 \) into the equation: \[ \text{Mean} = \frac{n}{1} = n \] - Thus, the value of \( n \) is the same as the mean.
Step 4: Conclusion Based on the given information, the value of \( n \) corresponds to the number of throws, and the correct answer is \( \boxed{3} \).