Question

1. a die is rolled once and turns up a 4. which statement is true about rolling a 3? a the experimental probability is 0 and the theoretical probability is 1/6. b the experimental probability is 1 and the theoretical probability is 1/6. c the experimental probability is 1/6 and the theoretical probability is 1/6. d the experimental probability is 1 and the theoretical probability is 1.

Explanation:

Step1: Define experimental probability

Experimental probability is based on actual results of an experiment. Since in this single - roll experiment a 3 did not come up, the number of times 3 occurred is 0. The total number of trials is 1. So the experimental probability $P_{exp}=\frac{0}{1} = 0$.

Step2: Define theoretical probability

A fair die has 6 faces numbered from 1 to 6. The theoretical probability of rolling any single number (in this case 3) is the number of favorable outcomes (1, since there is one 3 on the die) divided by the total number of possible outcomes (6). So the theoretical probability $P_{theo}=\frac{1}{6}$.

Answer:

A. The experimental probability is 0 and the theoretical probability is $\frac{1}{6}$