Total tyres recorded equal 1000. The required probabilities are: (i) 20 / 1000 = 0.02, (ii) (210 + 325) / 1000 = 535 / 1000 = 0.535 and (iii) 445 / 1000 = 0.445.
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(i) S = {HH, HT, TH, TT}, P(at least 1 head) = 3/4. (ii) S = {1, 2, …, 10}, P(even) = 5/10 = 1/2. (iii) S = {1, 2, 3, 4, 5, 6}, P(> 4) = 2/6 = 1/3. (iv) P(not red) ...
(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 = ...
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.
The probability for Arts Club is 11 / 40 = 0.275 (27.5%). The sample proportion for Sports Club is 9 / 40. Across 800 students, the estimated count is (9 / 40) x 800 = 180 students.