Question

I roll two dice simultaneously. Classify the probability that the number on the first die is a multiple of 2 and the number on the second die is a multiple of 3.
Likely
Unlikely
Certain
Impossible

Answer 1

To determine the probability that the number on the first die is a multiple of 2 and the number on the second die is a multiple of 3, we can analyze the possible outcomes for each die:

1. **First Die (multiple of 2)**: The numbers on a standard die are 1, 2, 3, 4, 5, and 6. The multiples of 2 in this range are 2, 4, and 6. Therefore, there are 3 favorable outcomes for the first die.

2. **Second Die (multiple of 3)**: The multiples of 3 on a standard die are 3 and 6. Thus, there are 2 favorable outcomes for the second die.

Now, let's calculate the total outcomes when rolling two dice:
The total number of outcomes is \(6 \times 6 = 36\) since each die has 6 faces.

Next, we find the number of favorable outcomes for the event where the first die shows a multiple of 2 and the second die shows a multiple of 3:

- For the first die (multiple of 2), we have 3 options: (2, 4, 6).
- For the second die (multiple of 3), we have 2 options: (3, 6).

Thus, the total number of favorable outcomes is:
\[ 3 \text{ (for the first die)} \times 2 \text{ (for the second die)} = 6 \text{ favorable outcomes.} \]

Therefore, the probability that the first die is a multiple of 2 and the second die is a multiple of 3 is:
\[
\text{Probability} = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{6}{36} = \frac{1}{6}.
\]

Since the probability of this event is not certain (1), nor impossible (0), but rather something in between, we can classify the event as **unlikely**.