List outcomes, compare equal and unequal chances and use recorded frequencies to estimate likelihoods.
Example 1
A fair 8−sided die is labelled 1 to 8, once each. What fraction of its equally likely outcomes show 2?
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Answer: 81
- There are 8 equally likely numbered outcomes.
- Only one is 2, so the fraction is 81.
Example 2
A fair coin gave 24 heads in 40 trials. Which statement is justified?
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Answer: Fair coins can give unequal counts in a finite set of trials.
- Each toss is uncertain; equal likelihood does not force equal recorded counts.
- The results describe these 40 trials and do not determine the next toss.
Example 3
A fair coin gave 21 heads in 40 trials. Which statement is justified?
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Answer: Fair coins can give unequal counts in a finite set of trials.
- Each toss is uncertain; equal likelihood does not force equal recorded counts.
- The results describe these 40 trials and do not determine the next toss.