INSURANCE AND GAMBLING.
§§ 1, 2. The certainties and uncertainties of life.
3–5. Insurance a means of diminishing the uncertainties.
6, 7. Gambling a means of increasing them.
8, 9. Various forms of gambling.
10, 11. Comparison between these practices.
12–14. Proofs of the disadvantage of gambling:—
(1) on arithmetical grounds:
15, 16. Illustration from family names.
17. (2) from the ‘moral expectation’.
18, 19. Inconclusiveness of these proofs.
20–22. Broader questions raised by these attempts.
[CHAPTER XVI.]
APPLICATION OF PROBABILITY TO TESTIMONY.
§§ 1, 2. Doubtful applicability of Probability to testimony.
3. Conditions of such applicability.
4. Reasons for the above conditions.
5, 6. Are these conditions fulfilled in the case of testimony?
7. The appeal here is not directly to statistics.
8, 9. Illustrations of the above.
10, 11. Is any application of Probability to testimony valid?
[CHAPTER XVII.]
CREDIBILITY OF EXTRAORDINARY STORIES.
§ 1. Improbability before and after the event.
2, 3. Does the rejection of this lead to the conclusion that the credibility of a story is independent of its nature?
4. General and special credibility of a witness.
5–8. Distinction between alternative and open questions, and the usual rules for application of testimony to each of these.
9. Discussion of an objection.
10, 11. Testimony of worthless witnesses.
12–14. Common practical ways of regarding such problems.
15. Extraordinary stories not necessarily less probable.
16–18. Meaning of the term extraordinary, and its distinction from miraculous.
19, 20. Combination of testimony.
21, 22. Scientific meaning of a miracle.
23, 24. Two distinct prepossessions in regard to miracles, and the logical consequences of these.
25. Difficulty of discussing by our rules cases in which arbitrary interference can be postulated.
26, 27. Consequent inappropriateness of many arguments.
[CHAPTER XVIII.]
ON THE NATURE AND USE OF AN AVERAGE, AND ON THE DIFFERENT KINDS OF AVERAGE.
§:nbsp;1. Preliminary rude notion of an average,
2. More precise quantitative notion, yielding
(1) the Arithmetical Average,
3. (2) the Geometrical.
4. In asymmetrical curves of error the arithmetic average must be distinguished from,
5. (3) the Maximum Ordinate average,
6. (4) and the Median.
7. Diagram in illustration.
8–10. Average departure from the average, considered under the above heads, and under that of
11. (5) The (average of) Mean Square of Error,
12–14. The objects of taking averages.
15. Mr Galton's practical method of determining the average.
16, 17. No distinction between the average and the mean.
18–20. Distinction between what is necessary and what is experimental here.
21, 22. Theoretical defects in the determination of the ‘errors’.
23. Practical escape from these.
(Note about the units in the exponential equation and integral.)