Experimental probability is 3/12 = 1/4 = 0.25, while theoretical probability is 1/6 (about 0.167). They differ due to a small trial sample; with 6000 rolls, experimental probability approaches theoretical probability by the Law of Large Numbers.
Suppose you roll a 6-sided die 12 times and get a ‘3’ three times. (i) What is the experimental probability of rolling a ‘3’? (ii) What is the theoretical probability of rolling a ‘3’? (iii) Why might these probabilities be different? What would you expect to happen if you roll the die 60, 600, or 6000 times?
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