To find the probability of the coin landing on tails and the number cube landing on an even number, let's first determine the total number of possible outcomes when flipping the coin and rolling the number cube.
- The coin has 2 possible outcomes: Heads (H) or Tails (T).
- The six-sided cube has 6 possible outcomes: 1, 2, 3, 4, 5, or 6.
So, the total number of outcomes when flipping the coin and rolling the cube is:
\[ 2 \times 6 = 12 \]
Next, we will identify the successful outcomes for the event of interest: the coin landing on tails (T) and the number cube landing on an even number (which are 2, 4, and 6).
The possible outcomes for tails (T) in combination with the even numbers are:
- T, 2
- T, 4
- T, 6
Thus, there are 3 successful outcomes: T, 2; T, 4; and T, 6.
Now we can calculate the probability:
\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{3}{12} = \frac{1}{4} \]
Therefore, the final answer is:
\[ \text{Probability of the coin landing on tails and the number cube landing on an even number} = \frac{1}{4} \]
If there are options (A, B, C, D) in the question and one of them specifies \(\frac{1}{4}\), that would be the correct answer. If you have specific options listed under A, B, C, and D, please provide them for a more precise match.