A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer:



Answer :

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].