Question

I roll two dice simultaneously. Classify the probability that the number on the first die is less than 3 and the number on the second die is less than 5.
Likely
Unlikely
Impossible
Certain

Answer 1

To classify the probability that the number on the first die is less than 3 and the number on the second die is less than 5, let's analyze the conditions.

1. **First Die**: The first die can show either a 1 or a 2 to satisfy the condition of being less than 3. This gives us 2 possible outcomes (1, 2).

2. **Second Die**: The second die can show a 1, 2, 3, or 4 to satisfy the condition of being less than 5. This gives us 4 possible outcomes (1, 2, 3, 4).

Now, we find the total combinations for these conditions:

- The number of outcomes for the first die is 2 (less than 3).
- The number of outcomes for the second die is 4 (less than 5).

To find the total favorable outcomes, you multiply the possible outcomes:

\[
2 \text{ (first die)} \times 4 \text{ (second die)} = 8
\]

Next, we consider the total possible outcomes when rolling two six-sided dice, which is:

\[
6 \text{ (first die)} \times 6 \text{ (second die)} = 36
\]

Now, we can classify the probability of the event that the first die is less than 3 and the second die is less than 5:

The probability is given by the ratio of favorable outcomes to possible outcomes:

\[
P(\text{First die < 3 and Second die < 5}) = \frac{8}{36} = \frac{2}{9}
\]

Since \(\frac{2}{9}\) is greater than 0 but less than 1, the event is neither certain nor impossible, and it is more likely than not to occur.

**Classification**: Unlikely.