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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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.
The word PEACE has 5 letters: P, E, A, C, E. (i) Letters P, E, C occur 4 times, giving probability 4 / 5 = 0.8. (ii) Non-E letters are P, A, C (3 letters), giving probability 3 / 5 ...
With 2 shirt options and 3 pants choices, multiplying 2 x 3 produces 6 possible outfit combinations: (Red, Jeans), (Red, Khakis), (Red, Shorts), (Blue, Jeans), (Blue, Khakis) and (Blue, Shorts).
(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) ...