List (iv) {0, 1, 2, 3} is the correct sample space because three tossed coins can yield 0, 1, 2 or 3 heads. The other lists either omit possible outcomes or include an impossible outcome.
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A coin has outcomes {H, T} and the cards have numbers {1, 2, 3, 4, 5, 6}. The complete sample space consists of 12 pairs: S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, ...
With replacement, tree branches into 4 paths then 4 paths each, creating 16 pairs (size 16). Without replacement, first draw branches into 4 paths then 3 paths each, creating 12 pairs (size 12).
(i) Primes 7 and 11 give 8 pairs, P = 8/36 = 2/9. (ii) P(different) = 1 – P(same) = 1 – 13/36 = 23/36. (iii) Favourable outcomes {HHT, HTH}, P = 2/8 = 1/4. (iv) Last digit 2 or 4, P = ...
For two dice, maximum sum is 12. An event with probability 0 is getting a sum of 13. An outcome or event with probability 1 is getting a sum between 2 and 12.