Question

You roll a 6-sided die.




What is P(5 or prime)?

Simplify your answer and write it as a fraction or whole number.

Answer 1

To find the probability \( P(5 \text{ or prime}) \), we first identify the outcomes on a 6-sided die and the relevant events.

The possible outcomes when rolling a 6-sided die are:
1, 2, 3, 4, 5, 6

Next, let's determine which outcomes are either 5 or a prime number. The prime numbers from 1 to 6 are:
- 2 (a prime number)
- 3 (a prime number)
- 5 (given in the problem)
- 6 is not a prime number
- 1 is not a prime number

So, the numbers that satisfy the condition "5 or prime" are:
- 5
- 2
- 3

The favorable outcomes are: 2, 3, and 5. Therefore, the total number of favorable outcomes is 3.

The total number of possible outcomes when rolling the die is 6 (1, 2, 3, 4, 5, 6).

Now we can find the probability:
\[
P(5 \text{ or prime}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{3}{6}
\]

Simplifying the fraction:
\[
P(5 \text{ or prime}) = \frac{1}{2}
\]

Thus, the simplified probability is:
\[
\boxed{\frac{1}{2}}
\]