To solve this problem, we need to find the probability that the number rolled on a standard die is less than 3. Here's a detailed, step-by-step solution:
### Step 1: Understand the Problem
A standard die has 6 faces, numbered from 1 to 6. We are asked to find the probability of rolling a number that is less than 3.
### Step 2: Determine the Total Number of Outcomes
Since a standard die has 6 faces, the total number of possible outcomes when rolling the die is 6.
### Step 3: Identify the Favorable Outcomes
The favorable outcomes are the numbers on the die that are less than 3. These numbers are:
- 1
- 2
So, there are 2 favorable outcomes.
### Step 4: Calculate the Probability
Probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6}
\][/tex]
### Step 5: Simplify the Fraction
The fraction [tex]\(\frac{2}{6}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
### Step 6: Convert the Fraction to a Decimal
To express the probability as a decimal, divide the numerator by the denominator:
[tex]\[
\frac{1}{3} \approx 0.333333
\][/tex]
### Final Answer
The probability that the number rolled is less than 3 is:
- As a simplified fraction: [tex]\(\frac{1}{3}\)[/tex]
- As a decimal rounded to the nearest millionth: [tex]\(0.333333\)[/tex]
So, the detailed, step-by-step solution concludes that the probability of rolling a number less than 3 on a standard die is [tex]\(\frac{1}{3}\)[/tex] or [tex]\(0.333333\)[/tex].
