Final answer:
a. The experimental probability of landing on a 2 is 1/6.
b. The experimental probability of not landing on a 6 is 7/8.
c. The experimental probability of landing on a 2 matches its theoretical probability.
d. The experimental probability of not landing on a 6 does not match its theoretical probability.
Step-by-step explanation:
The question involves calculating experimental probability and comparing it with theoretical probability. Experimental probability is determined by the outcomes of an actual experiment, while theoretical probability is based on the expected outcomes in a perfect theoretical situation without any practical constraints.
Part a:
The experimental probability of landing on a 2 is computed by dividing the number of times it landed on 2 by the total number of rolls. Since the number cube landed on 2 four times out of 24 rolls, the experimental probability is 4/24 or 1/6 when simplified.
Part b:
The experimental probability of not landing on a 6 is calculated by subtracting the number of times it landed on 6 from the total number of rolls and then dividing by the total rolls. Since it landed on 6 three times, the probability of not landing on a 6 is (24 - 3)/24 = 21/24 or 7/8 when simplified.
Part c:
To compare the experimental probability from part a to the theoretical probability, note that theoretically, a fair six-sided die has an equal chance of landing on any one of its six faces. Thus, the theoretical probability of landing on any specific number, including a 2, is 1/6.
Part d:
Similarly, the theoretical probability of not landing on a 6 is 5/6, because there are five other faces that are not a 6. Thus, each of these faces has a theoretical probability of 1/6, and combined give 5/6.