Question

An unfair die marked with 1, 2, 2, 3, 4, 6 is thrown. Which of the following events is most unlikely to happen?
Getting a multiple of 2
Getting an even number
Getting a multiple of 4
Getting a multiple of 3

Answer 1

To determine which event is most unlikely to happen when rolling the unfair die marked with 1, 2, 2, 3, 4, and 6, we first need to evaluate the probabilities for each event.

1. **Getting a multiple of 2:**
- The multiples of 2 from the die are: 2, 2, 4, and 6.
- Count: 4 outcomes (2 occurs twice).
- Probability: \( \frac{4}{6} = \frac{2}{3} \).

2. **Getting an even number:**
- The even numbers on the die are: 2, 2, 4, and 6.
- Count: 4 outcomes (2 occurs twice).
- Probability: \( \frac{4}{6} = \frac{2}{3} \).

3. **Getting a multiple of 4:**
- The multiples of 4 from the die are: 4.
- Count: 1 outcome.
- Probability: \( \frac{1}{6} \).

4. **Getting a multiple of 3:**
- The multiples of 3 from the die are: 3 and 6.
- Count: 2 outcomes.
- Probability: \( \frac{2}{6} = \frac{1}{3} \).

Now, summarizing the probabilities:

- Getting a multiple of 2: \( \frac{2}{3} \)
- Getting an even number: \( \frac{2}{3} \)
- Getting a multiple of 4: \( \frac{1}{6} \)
- Getting a multiple of 3: \( \frac{1}{3} \)

The event that is most unlikely to happen is getting a **multiple of 4** since it has the lowest probability of \( \frac{1}{6} \).