Final answer:
The question about the probability of getting a 50% coupon when rolling a die cannot be determined without experimental data. Options given do not match the theoretical probability of 1/6 for a fair die. Additionally, for two independent events A and B, the probability of both occuring is P(A) * P(B). For mutually exclusive events, it's always 0 since they can't occur simultaneously.
Step-by-step explanation:
The experimental probability of receiving a 50% coupon after rolling the number cube 20 times cannot be determined without data from the actual experiment. However, using theoretical probability, we generally assume that each side of a six-sided die has an equal chance of 1/6 to roll. If a 50% coupon is related to one particular side, then the theoretical probability of rolling that side is 1/6, not any of the options given (A. 0.10, B. 0.20, C. 0.25, D. 0.50).
For question 70, since events A and B are independent, the probability P(A AND B) is found by multiplying their individual probabilities: P(A) * P(B) = 0.2 * 0.3 = 0.06. So, the answer is D. 0.06.
Regarding question 72, if events H and D are mutually exclusive, they cannot occur at the same time, which means P(H AND D) = 0, and the correct answer is B. 0.
Remember, when dealing with probabilities and experiments, it's crucial to round answers to four decimal places for precision and to follow the instructions for the experimental or theoretical calculation closely.
Experiments such as rolling dice or flipping coins demonstrate the law of large numbers, as in Pearson's coin-tossing experiment, showing that the long-term results converge on the theoretical probability.