Question

Suppose you roll a 6-sided die 12 times and get a ‘3’ three times.

Accepted Answer

(i) Experimental Probability = (Number of times '3' occurs) / (Total number of trials) = 3 / 12 = 1/4 or 0.25. (ii) Theoretical Probability = (Number of favorable outcomes) / (Total possible outcomes). The sample space for a 6-sided die is S = 1, 2, 3, 4, 5, 6. The event of rolling a '3' has 1 favorable outcome. So, P(3) = 1/6 ≈ 0.166 or 16.6%. (iii) These probabilities might be different because the experimental probability is based on a small number of trials, where random variations can easily occur. Each roll of the die is an independent event. If we roll the die 60, 600, or 6000 times, we would expect the experimental probability to get closer to the theoretical probability of 1/6. — The experimental probability is derived from the actual outcomes of the experiment (3 '3's out of 12 rolls), while the theoretical probability is derived from the sample space (1 favorable outcome out of 6 possible outcomes). Differences in small sample sizes occur due to random chance, as each roll is an independent event. As the number of trials increases, the experimental probability tends to approach the theoretical probability.

Explanation

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