(i) S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T} with 12 outcomes. (ii) S = {-4, -3, -2, -1, 0, 1, 2, 3, 4}. (iii) By color, S = {Green, Red}; by distinct balls, S = ...
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When rolling a standard 6-sided die, the sample space comprises {1, 2, 3, 4, 5, 6}. Each face represents a distinct possible result, so the total number of possible outcomes in the sample space is 6.
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.
When rolling a 6-sided die, sample space is {1, 2, 3, 4, 5, 6}, giving 6 possible outcomes. The even numbers are 2, 4, and 6, so probability is 3/6 = 1/2 = 0.5.
For 100 tosses yielding 7 bottom landings, 18 top landings, and 75 side landings, the experimental probabilities are P(bottom) = 7/100 = 0.07, P(top) = 18/100 = 0.18, and P(side) = 75/100 = 0.75.