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 is 1/6, since there is one 3 on the cube out of six possible outcomes.

b. The experimental probability of rolling a 3 is 67/450, since out of the 450 rolls, 67 resulted in a 3.

To find the theoretical probability of rolling a 3, we need to know the total number of possible outcomes and the number of favorable outcomes.

a. The total number of possible outcomes when rolling a number cube is 6 (since there are 6 sides). The number of favorable outcomes (rolling a 3) is 1. Therefore, the theoretical probability of rolling a 3 is 1/6.

To find the experimental probability of rolling a 3, we use the formula:

Experimental Probability = (Number of favorable outcomes) / (Total number of trials)

b. The number of favorable outcomes (rolling a 3) is given as 67. The total number of trials is given as 450. Therefore, the experimental probability of rolling a 3 is 67/450.

So, the answers are:

a. The theoretical probability of rolling a 3 is 1/6.
b. The experimental probability of rolling a 3 is 67/450.