Answer :
To determine the probability of rolling a 4 on a six-sided die and then rolling an even number on a six-sided die, we need to follow a systematic approach. Here’s a step-by-step solution:
1. Identify the probability of rolling a 4 on a six-sided die:
A standard die has six faces, each with a unique number from 1 to 6. The probability of rolling any specific number, such as a 4, is given by:
[tex]\[ \text{Probability of rolling a 4} = \frac{1}{6} \][/tex]
2. Identify the probability of rolling an even number on a six-sided die:
A standard die has three even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is:
[tex]\[ \text{Probability of rolling an even number} = \frac{3}{6} = \frac{1}{2} \][/tex]
3. Calculate the probability of both events occurring in sequence:
Since the events (rolling a 4 and then rolling an even number) are independent, you multiply their respective probabilities together:
[tex]\[ \text{Probability of both events} = \left(\frac{1}{6}\right) \times \left(\frac{1}{2}\right) = \frac{1}{12} \][/tex]
Therefore, the probability of first rolling a 4 on a six-sided die and then rolling an even number is:
[tex]\[ \boxed{\frac{1}{12}} \][/tex]
So, the correct choice from the given options is D. 1/12.
1. Identify the probability of rolling a 4 on a six-sided die:
A standard die has six faces, each with a unique number from 1 to 6. The probability of rolling any specific number, such as a 4, is given by:
[tex]\[ \text{Probability of rolling a 4} = \frac{1}{6} \][/tex]
2. Identify the probability of rolling an even number on a six-sided die:
A standard die has three even numbers: 2, 4, and 6. Therefore, the probability of rolling an even number is:
[tex]\[ \text{Probability of rolling an even number} = \frac{3}{6} = \frac{1}{2} \][/tex]
3. Calculate the probability of both events occurring in sequence:
Since the events (rolling a 4 and then rolling an even number) are independent, you multiply their respective probabilities together:
[tex]\[ \text{Probability of both events} = \left(\frac{1}{6}\right) \times \left(\frac{1}{2}\right) = \frac{1}{12} \][/tex]
Therefore, the probability of first rolling a 4 on a six-sided die and then rolling an even number is:
[tex]\[ \boxed{\frac{1}{12}} \][/tex]
So, the correct choice from the given options is D. 1/12.
