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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(i) Experimental probability = Number of 3s / Total rolls = 3 / 12 = 1 / 4 = 0.25 (or 25%).
(ii) Theoretical probability = 1 / 6 (approximately 0.167 or 16.7%).
(iii) They differ because 12 is a small number of trials where random variation is significant. By the Law of Large Numbers, as trials increase to 60, 600, or 6000, experimental probability gets closer and closer to theoretical probability of 1 / 6.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 7 The Mathematics of Maybe: Introduction to Probability Question Answer (2026-27)
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