To solve this problem, we need to find the probability of two independent events occurring in succession: rolling an even number on the first roll and rolling a number greater than 4 on the second roll.
### Step 1: Determine the probability of rolling an even number on the first roll
A six-sided cube has the numbers 1, 2, 3, 4, 5, and 6. The even numbers among these are 2, 4, and 6. Thus, there are 3 even numbers out of a total of 6 possible outcomes.
To calculate the probability of rolling an even number:
[tex]\[ P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total number of outcomes}} = \frac{3}{6} = 0.5 \][/tex]
### Step 2: Determine the probability of rolling a number greater than 4 on the second roll
The numbers greater than 4 on a six-sided cube are 5 and 6. Thus, there are 2 numbers greater than 4 out of a total of 6 possible outcomes.
To calculate the probability of rolling a number greater than 4:
[tex]\[ P(\text{greater than 4}) = \frac{\text{Number of outcomes greater than 4}}{\text{Total number of outcomes}} = \frac{2}{6} \approx 0.3333 \][/tex]
### Step 3: Calculate the probability of both events occurring
Since rolling the cube the first time and the second time are independent events, the probability of both events occurring is the product of their individual probabilities.
Therefore:
[tex]\[ P(\text{even on first roll and greater than 4 on second roll}) = P(\text{even}) \times P(\text{greater than 4}) \][/tex]
[tex]\[ = 0.5 \times 0.3333 \approx 0.1667 \][/tex]
### Step 4: Convert the probability to a fraction for the answer choices
The probability 0.1667 corresponds to:
[tex]\[ \frac{1}{6} \][/tex]
Thus, the correct answer is [tex]\(\boxed{\frac{1}{6}}\)[/tex].
