(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) ...
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Experiments (ii), (iii) and (v) have equally likely outcomes due to symmetry and equal chance. Experiments (i) and (iv) are not equally likely because mechanical conditions bias car starting and blue marbles outnumber red ones.
The correct term is relative frequency and its value is 15 / 50 = 3 / 10 = 0.3. While 15 is the absolute count (frequency), dividing by the total 50 students gives the relative frequency.
The answers are: (i) 0, (ii) sample space, (iii) 1 and (iv) 1/2 (or 0.5). These represent fundamental probability values: 0 denotes impossibility, 1 indicates certainty and an unbiased coin yields an even chance of 0.5.
With replacement, total pens = 9. Outcomes for colors are RR, RB, RG, BR, BB, BG, GR, GB, GG. The probability of both picking the same color is P(RR) + P(BB) + P(GG) = 9/81 + 16/81 + 4/81 = ...