What is the probability of rolling an even number on the first die and a two on the second die? Write your answer as a fraction or a whole number. With fractions, use a slash ( / ) to separate the numerator and denominator.

Answer 1

To find the probability of rolling an even number on the first die and a two on the second die, we can analyze each part of the event:

1. Rolling an even number on the first die: A standard die has six faces (1, 2, 3, 4, 5, 6). The even numbers on a die are 2, 4, and 6. Therefore, there are 3 even numbers out of 6 total numbers. The probability of rolling an even number on the first die is: \[ P(\text{even on first die}) = \frac{3}{6} = \frac{1}{2} \]

2. Rolling a two on the second die: Again, a standard die has six faces. Only one of these faces shows the number 2. Therefore, the probability of rolling a two on the second die is: \[ P(\text{two on second die}) = \frac{1}{6} \]

3. Calculating the joint probability: Since the outcome of rolling the first die is independent of the outcome of rolling the second die, we can multiply their probabilities: \[ P(\text{even on first die and two on second die}) = P(\text{even on first die}) \times P(\text{two on second die}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} \]

Thus, the probability of rolling an even number on the first die and a two on the second die is: \[ \frac{1}{12} \]