Question

An unfair die has six sides marked with 1, 2, 1, 4, 5, 1. If the die is thrown once, which of the following events is most unlikely to happen?
Getting a number 1
Getting a number 2
Getting an even number
Getting an odd number

Answer 1

To assess the likelihood of each event when throwing the unfair die with faces marked 1, 2, 1, 4, 5, 1, we can analyze the frequency of each outcome.

1. **Getting a number 1**: The faces of the die contain three 1s.
- Probability: \( P(1) = \frac{3}{6} = \frac{1}{2} \)

2. **Getting a number 2**: The die has only one face with the number 2.
- Probability: \( P(2) = \frac{1}{6} \)

3. **Getting an even number**: The even numbers on the die are 2 and 4.
- The faces showing even numbers are 2 (1 time) and 4 (1 time), so there are a total of 2 even faces.
- Probability: \( P(\text{even}) = \frac{2}{6} = \frac{1}{3} \)

4. **Getting an odd number**: The odd numbers on the die are 1, 1, 1, and 5.
- The faces showing odd numbers are 1 (3 times) and 5 (1 time), hence there are a total of 4 odd faces.
- Probability: \( P(\text{odd}) = \frac{4}{6} = \frac{2}{3} \)

Now we can summarize the probabilities:

- Probability of getting a 1: \( \frac{1}{2} \)
- Probability of getting a 2: \( \frac{1}{6} \)
- Probability of getting an even number: \( \frac{1}{3} \)
- Probability of getting an odd number: \( \frac{2}{3} \)

The event "Getting a number 2" has the lowest probability of \( \frac{1}{6} \), making it the most unlikely event among the options given.

Thus, the most unlikely event to happen is **Getting a number 2**.