Question

tammy rolled a number cube 200 times and got the following results.

outcome rolled	1	2	3	4	5	6

fill in the table below. round your answers to the nearest thousandth.
(a) from tammys results, compute the experimental probability of rolling a 6.

(b) assuming that the cube is fair, compute the theoretical probability of rolling a 6.

(c) assuming that the cube is fair, choose the statement below that is true:

• as the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
• as the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.
• the experimental and theoretical probabilities must always be equal.

Explanation:

Step1: Calculate experimental probability

Experimental probability is the number of times 6 was rolled divided by total rolls.
$\text{Experimental Probability} = \frac{40}{200} = 0.200$

Step2: Calculate theoretical probability

For a fair cube, there is 1 favorable outcome (6) out of 6 total outcomes.
$\text{Theoretical Probability} = \frac{1}{6} \approx 0.167$

Step3: Identify true probability statement

By the law of large numbers, more trials make experimental probability approach theoretical probability.

Answer:

(a) $0.200$
(b) $0.167$
(c) As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.