UpStudy Free Solution:

To determine the probability of rolling a prime number on a 6-sided die, we first identify the prime numbers within the range of possible outcomes (1 through 6). The prime numbers in this range are 2, 3, and 5.

Next, we count the number of prime numbers:

2

3

5

There are 3 prime numbers.

Since a 6-sided die has 6 possible outcomes, the probability \(P\) of rolling a prime number is given by the ratio of the number of prime numbers to the total number of possible outcomes.

Thus, the probability \(P\) is:

\[P( \text { prime} ) = \frac { \text { Number of prime outcomes} } { \text { Total number of outcomes} } = \frac { 3} { 6} \]

We can simplify this fraction:

\[P( \text { prime} ) = \frac { 3} { 6} = \frac { 1} { 2} \]

So, the probability of rolling a prime number on a 6-sided die is:

\[\boxed{ \frac { 1} { 2} } \]

Supplemental Knowledge

To determine the probability of rolling a prime number on a 6-sided die, we need to identify the prime numbers within the range of possible outcomes (1 to 6). A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The possible outcomes when rolling a 6-sided die are: \(\{ 1, 2, 3, 4, 5, 6\} \).

Join millions who rely on UpStudy for all of their educational needs and enhance your understanding with UpStudy today!