Question

what is the theoretical probability of of rolling a number divisible by 3 on a 15 fair sided die rounded to the nearest tenth

Answer 1

To find the theoretical probability of rolling a number divisible by 3 on a 15-sided die, we first need to determine how many of the possible outcomes (the numbers 1 through 15) are divisible by 3.

The numbers from 1 to 15 that are divisible by 3 are:
- 3
- 6
- 9
- 12
- 15

So, there are 5 numbers (3, 6, 9, 12, and 15) that meet this condition.

The total number of possible outcomes when rolling a 15-sided die is 15.

The probability \( P \) of rolling a number divisible by 3 is given by the formula:

\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{5}{15}
\]

Simplifying this fraction gives:

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

To express this probability as a decimal, we calculate:

\[
\frac{1}{3} \approx 0.3333
\]

When rounding to the nearest tenth, this becomes:

\[
0.3
\]

Thus, the theoretical probability of rolling a number divisible by 3 on a 15-sided die, rounded to the nearest tenth, is **0.3**.