Discover a wealth of information and get your questions answered on IDNLearn.com. Our experts are ready to provide prompt and detailed answers to any questions you may have.
Sagot :
To determine the probability that Ethan rolls a number less than 3 on a 6-sided number cube, let's break down the problem step by step:
1. Identify the Total Number of Possible Outcomes:
- A 6-sided number cube has 6 faces, each with a distinct number from 1 to 6.
- Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the Favorable Outcomes:
- We are interested in rolling a number that is less than 3.
- The numbers on the cube that are less than 3 are 1 and 2.
- Hence, there are 2 favorable outcomes.
3. Calculate the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability \( P \) of rolling a number less than 3 is given by:
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction:
- Simplify \(\frac{2}{6}\) 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]
Therefore, the probability that Ethan rolls a number less than 3 is \(\frac{1}{3}\).
The correct answer is:
D. [tex]\(\frac{1}{3}\)[/tex]
1. Identify the Total Number of Possible Outcomes:
- A 6-sided number cube has 6 faces, each with a distinct number from 1 to 6.
- Therefore, the total number of possible outcomes when rolling the cube is 6.
2. Identify the Favorable Outcomes:
- We are interested in rolling a number that is less than 3.
- The numbers on the cube that are less than 3 are 1 and 2.
- Hence, there are 2 favorable outcomes.
3. Calculate the Probability:
- Probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability \( P \) of rolling a number less than 3 is given by:
[tex]\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{6} \][/tex]
4. Simplify the Fraction:
- Simplify \(\frac{2}{6}\) 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]
Therefore, the probability that Ethan rolls a number less than 3 is \(\frac{1}{3}\).
The correct answer is:
D. [tex]\(\frac{1}{3}\)[/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.