Questions: Counting and Probability Experimental and theoretical probability Lashonda rolled a number cube 500 times and got the following results. Outcome Rolled: 1, 2, 3, 4, 5, 6 Number of Rolls: 89, 75, 92, 69, 91, 84 Answer the following. Round your answers to the nearest thousandths. (a) From Lashonda's results, compute the experimental probability of rolling a 1. (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 1.

Solution Steps

To solve these problems, we need to understand the difference between experimental and theoretical probability.

(a) The experimental probability is calculated by dividing the number of times the event occurred by the total number of trials. In this case, we divide the number of times a 1 was rolled by the total number of rolls.

(b) The theoretical probability assumes that all outcomes are equally likely. For a fair six-sided die, the probability of rolling any specific number is 1 divided by the number of sides on the die.

The experimental probability is calculated by dividing the number of times the event occurred by the total number of trials. For rolling a 1, this is given by:

\[ P_{\text{exp}}(1) = \frac{\text{Number of times 1 was rolled}}{\text{Total number of rolls}} = \frac{89}{500} = 0.178 \]

The theoretical probability assumes that all outcomes are equally likely. For a fair six-sided die, the probability of rolling any specific number is:

\[ P_{\text{theo}}(1) = \frac{1}{6} \approx 0.1667 \]

Final Answer