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 ...
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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.
Labeling fruits as A1, O1, O2 for basket A and B1, M1 for basket B gives 6 equally likely outcomes. The sample space is {(A1, B1), (A1, M1), (O1, B1), (O1, M1), (O2, B1), (O2, M1)}. P(Apple, Banana) = 1/6.
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.
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.