Question

a number cube numbered 1 - 6 is rolled once. what is the probability that the side facing up shows a 4?
options:
\\(\frac{4}{6}\\)
\\(\frac{1}{4}\\)
1
another option partially visible

Explanation:

Step1: Identify total outcomes

A number cube (die) numbered 1 - 6 has 6 possible outcomes when rolled: 1, 2, 3, 4, 5, 6. So total outcomes \( n = 6 \).

Step2: Identify favorable outcomes

We want the side showing 4. There's only 1 side with 4, so favorable outcomes \( m = 1 \).

Step3: Calculate probability

Probability \( P \) is given by the formula \( P=\frac{\text{favorable outcomes}}{\text{total outcomes}} \). Substituting \( m = 1 \) and \( n = 6 \), we get \( P=\frac{1}{6} \)? Wait, no, wait the options: Wait the first option is \( \frac{4}{6} \)? Wait no, maybe I misread. Wait the problem: "A number cube numbered 1 - 6 is rolled once. What is the probability that the side facing up shows a 4?" Wait the options: first option \( \frac{4}{6} \)? No, wait the user's image: the first option is \( \frac{4}{6} \)? Wait no, maybe the options are: first \( \frac{4}{6} \), second \( \frac{1}{4} \), third \( 1 \), fourth \( \frac{1}{6} \)? Wait the user's image: let's re-express. Wait the problem is about probability of rolling a 4. So total outcomes 6, favorable 1, so probability \( \frac{1}{6} \). Wait but the first option is \( \frac{4}{6} \)? No, maybe the options are: first \( \frac{4}{6} \) (maybe a typo, or maybe I misread the number). Wait no, let's check again. Wait the number cube is 1 - 6. Rolling a 4: there's 1 four. So probability is \( \frac{1}{6} \). Wait but the options: if the fourth option is \( \frac{1}{6} \), then that's the answer. Wait the user's image: the options are: first \( \frac{4}{6} \), second \( \frac{1}{4} \), third \( 1 \), fourth \( \frac{1}{6} \)? So the correct probability is \( \frac{1}{6} \), which is the fourth option (assuming the fourth is \( \frac{1}{6} \)). Wait but let's do the steps again.

Wait total outcomes: 6 (1,2,3,4,5,6). Favorable: 1 (only 4). So probability \( P = \frac{1}{6} \). So the correct option is the one with \( \frac{1}{6} \).

Answer:

The option with \( \frac{1}{6} \) (assuming it's the fourth option in the list, e.g., if the options are: A. \( \frac{4}{6} \), B. \( \frac{1}{4} \), C. \( 1 \), D. \( \frac{1}{6} \), then the answer is D. \( \frac{1}{6} \))