Answer :
Sure, let's walk through the steps to find the probability of rolling a 4 or a 5 when a fair six-sided die is thrown once.
1. Total Outcomes: The first thing to recognize is that a die has 6 faces, each showing a different number from 1 to 6. Therefore, the total number of possible outcomes when rolling the die is 6.
2. Favorable Outcomes: Next, we identify the favorable outcomes. We are specifically interested in the die landing on either a 4 or a 5. Hence, there are 2 favorable outcomes (rolling a 4 or rolling a 5).
3. Calculate Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this problem, the number of favorable outcomes is 2.
- The total number of outcomes is 6.
The probability is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction: The fraction \(\frac{2}{6}\) 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]
5. Convert to Decimal (Optional): Converting \(\frac{1}{3}\) to a decimal, we get approximately 0.333... (repeating).
Given the choices:
- \(1\)
- \(\frac{2}{6}\)
- \(\frac{4}{6}\)
- \(\frac{5}{6}\)
The correct choice that matches our calculated probability \(\frac{1}{3}\) (or \(\frac{2}{6}\)) is option B:
[tex]\[ \boxed{\frac{2}{6}} \][/tex]
1. Total Outcomes: The first thing to recognize is that a die has 6 faces, each showing a different number from 1 to 6. Therefore, the total number of possible outcomes when rolling the die is 6.
2. Favorable Outcomes: Next, we identify the favorable outcomes. We are specifically interested in the die landing on either a 4 or a 5. Hence, there are 2 favorable outcomes (rolling a 4 or rolling a 5).
3. Calculate Probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
- In this problem, the number of favorable outcomes is 2.
- The total number of outcomes is 6.
The probability is calculated as:
[tex]\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction: The fraction \(\frac{2}{6}\) 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]
5. Convert to Decimal (Optional): Converting \(\frac{1}{3}\) to a decimal, we get approximately 0.333... (repeating).
Given the choices:
- \(1\)
- \(\frac{2}{6}\)
- \(\frac{4}{6}\)
- \(\frac{5}{6}\)
The correct choice that matches our calculated probability \(\frac{1}{3}\) (or \(\frac{2}{6}\)) is option B:
[tex]\[ \boxed{\frac{2}{6}} \][/tex]
