Question

What is the probability of rolling a prime number?


1
6
6
1
​



1
2
2
1
​



5
6
6
5
​



1
3
3
1
​

Answer 1

To calculate the probability of rolling a prime number on a standard six-sided die, we first need to identify the prime numbers within the range of possible outcomes when rolling the die (which are the numbers 1 through 6).

The prime numbers between 1 and 6 are:
- 2
- 3
- 5

So, there are 3 prime numbers (2, 3, 5). The total number of outcomes when rolling a die is 6 (the numbers 1, 2, 3, 4, 5, 6).

The probability \( P \) of rolling a prime number is given by the formula:

\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]

In this case:

\[
P = \frac{3}{6} = \frac{1}{2}
\]

So, the probability of rolling a prime number on a standard six-sided die is \( \frac{1}{2} \) or 50%.