A number cube is rolled 450 times. The number 3 comes up 67 times.
a. What is the theoretical probability of rolling a 3? Write your answer as a fraction in simplest form.
b. What is the experimental probability of rolling a 3? Write your answer as a fraction in simplest form.
a. The theoretical probability of rolling a 3 on a number cube is $\frac{1}{6}$ since there is only one favorable outcome (rolling a 3) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).
b. The experimental probability of rolling a 3 is found by dividing the number of times a 3 came up by the total number of rolls: $\frac{67}{450}$. This can be simplified by dividing both the numerator and denominator by 5: $\frac{67}{450} = \frac{13}{90}$.