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The familiar familial fallacy extended

 

The original question on p5 was: Mr Brown has exactly two children. One of them is a boy what is the probability that the other is a girl. It was suggested that the answer should be 2/3.

 

I am grateful to Ged Dean for pointing out that there is another twist to this paradox. Suppose I argue like this. Let us consider Mr Brown’s son and consider the other child relative to him. This is either an older brother or a younger brother or an older sister or a younger sister. In two out of the four cases it is a boy. So the probability is one half after all.

 

This disagrees, of course, with the empirical evidence I presented on pages 6 and 8 but that evidence depends on the way I select the data: essentially sampling by fathers rather than by children. The former is implicit in the way the question was posed, implying sampling by father, but as no sampling process has been defined, you are entitled to think differently.

 

To illustrate the difference, let us take an island with four two-child families one of each of the four possible combinations: boy-boy, boy-girl, girl-boy and girl-girl. In this island it so happens that the oldest child has the name that begins with a letter earlier in the alphabet. The families are

 

Fred and Pete (father Bob)

Andrew and Susan (father Charles)

Anthea and Zack (father Dave)

Beatrice and Charlotte (father Ed)

 

Let us choose a father at random. There are three chances out of four that it is either Bob, Charles or Dave, who each have at least one son. Given that the father chosen has at least one boy there are two chances out of three that the father is either Charles or Dave and therefore that the other child is a girl. So, there is a probability of two thirds that the other child is a girl. This agrees with the previous solution.

 

Now, however, let us choose a child at random. There are four chances out of eight that it is a boy. If it is a boy, it is either Fred or Pete or Andrew or Zack. In two out of the four cases the other child is a boy.

 

To put it another way: given that the child we have chosen is a boy, what is the probability that the father is Bob? The answer is ‘one half’.


 

 

Dicing with Death misprints

 

Here is a list of misprints (or just plain errors), that, alas, found their way into the book. I am grateful to Catherine Cameron, Andy Garrett, Harold Henderson, Nick Holford, Kevin McConway, Chris McManus, John Nelder, Roger Pinkham, Stephen Stigler, Richard Wilschke and my mother, Elizabeth Senn, for pointing some of these out and in particular to Nick Cox and Leonard Finegold for very thorough examinations of the text.

 

 

1.      On the Permissions page

For the acknowledgements to Harper Collins, there should be a full stop after Ernestine Gilbreth Carey. The remaining words in that sentence should be replaced by a new sentence, as follows. 'Professor Edward Chaney: The Book of Ebenezer Le Page by GB Edwards.'

 

2.      On the Permissions page. Line -5 ‘Canongate’ not ‘Cannongate’.

 

3.      P5 Line 8 ‘feels’ not ‘feel’

 

4.      P10 Line 4 ‘?’ to end the sentence rather than ‘.’.

 

5.      P10 Line 16 ‘the long-run’ not ‘then long-run’.

 

6.      P12 Line -10 There is an unnecessary apostrophe after ‘Pearson’.

 

7.      P17 The two lines before the section The height of improbability should be amended to read:

have changed this now means that the first period values are lower than the second period ones. The accident rate is getting worse.’.

 

8.      P17 Line -5 should read, '...that men are on average 8% taller than women,..'. (Appropriately, the book is available on Amazon.)

 

9.      P18 Line 5 should read, 'Figure 1.5 above...'.

 

10.  P22 Line 1 should refer to ‘Figure 1.7 above..’

 

11.  P24 Line -15 unwanted comma after ‘diseases’.

 

12.  P32 Family tree. Should be Roman numerals for James I and John I

 

13.  P33 line -10/-9 should be ‘…John’s claim…’ not  …John claims…’

 

14.  P37 Line 14 should be 1/2 985 984 not 1/12 985 984

 

15.  P38 Line 5 ‘Kendall’ not ‘Kendal’.

 

16.  p39 Line -10 there is one ‘that’ too many

 

17.  P42 Line 4 right hand side of equation should be P(B)P(AB)

 

18.  P47 Line 6 Unnecessary comma after ‘Sewall Wright’.

 

19.  P47 Line -12 missing comma after ‘Gosset’.

 

20.  P48 Table 2.3 ‘Cushny’ not ‘cushny’.

 

21.  P48 Table 2.3. The figure under column headed 'A' against the row labelled 'mean' should be +.75 (that is to say +0.75) not +7.5.

 

22.  P48 First line. Missing comma after ‘(later at UCL of course)’.

 

23.  P50 First subheading. There is a space missing. Should be: TB or not TB

 

24.  P52 Line 8. ‘Haileybury’ not ‘Halibury’.

 

25.  P54 Line 9 Should be ‘streptomycin’ not ‘steptomycin’.

 

26.  P56, bottom of page I should have referred to the lady’s chances as being one in eight etc, rather than eight and so forth

 

27.  P55 Line 15 ‘Eponymy’ not ‘Eponomy’.

 

28.  .P68 Line 7 Comma after ‘Clinical Trials Listing Service’ to be deleted.

 

29.  P76  Line 17 Missing apostrophe in ‘St John’s’.

 

30.  P84 Line 9 ‘Berkeley’ not ‘Berkley’.

 

31.  P84 Line -13 ‘effect on’ not ‘effect of’

 

32.  P93 Line -16 ‘principal’ not ‘principle’.

 

33.  P93 line -9 there is one ‘that’ too many: should be ‘…that…’ not ‘…that that…

 

34.  P94 Line -8. Missing ‘?’ at end of first sentence.

 

35.  P98 Bottom three lines ‘cos C’ not ‘cosC’ and ‘Cos 90°’ not ‘Cos90°

 

36.  P99 first displayed equation should have c2 = (3 miles)2 + (4 miles)2 – 2 × 3 miles × 4 miles × -0.707

 

37.  P100 In equation (5.5) for both lines the second equals ( = ) sign should be a minus (-) sign, thus:

 

 

38.  P101 Line 18 Should read:  (5 miles)2+(12 miles)2= 25miles2 +144

miles2 =169 miles2 .

 

39.  P103 Line 13 ‘b’ (in italics) rather than ‘b’.

 

40.  P103 Second section heading:  A bout de souffle. (No acute accent. I would like to claim this as having been a clever joke but it is a printer’s error that has left me with egg on my face.)

 

41.  P104. Line 15 ‘differences’ (plural).

 

42.  P106 Two lines above section heading ‘Fair Sex’. Order of bracket and full stop incorrect. Should be ‘..as ‘confounders’.)’.

 

43.  P107 line -2 should be  a colon and not a semi-colon after platitude

 

44.  P110 Line 8 there is one ‘that’ too many: should be ‘…that…’ not ‘…that that…’

 

45.  P111 Line -8 replace ‘…Francis’s mother was the son…’ with, ‘…Francis’s mother was the daughter…’ (What with women being taller than men and being sons rather than daughters I seem to have suffered some confusion as regards sex.)

 

46.  P112 Line -6 should be ‘non-beliefs’ not ‘non beliefs’

 

47.  PP116-117 Kevin McConway has pointed out to me that the argument is rather obscure here. On reviewing it I agree and realise that I either needed to say a lot more or a lot less at this point. Anybody who wants a fuller explanation is welcome to email me! stephen@senns.demon.co.uk

 

48.  P117 First displayed equation. Subscript in OddsS should be somewhat larger for consistency with OddsN

 

49.  P119 line -5. The word ‘time’ should be removed from the end of the sentence.

 

50.  P128 Line -7 ‘until’ not ‘untill

 

51.  P129 Line -4 Halley not Haley

 

52.  P134 line 22     (9/10)n - 1   not (9/10)n – 1.

 

53.  P134 Line -5 Should be 0.066 not 0.66

 

54.  P136 Line 8 ‘Russian’ not ‘Rusian’.

 

55.  P141 Line 15 ‘principal’ not ‘principle’. (This is clearly a principal error of mine.)

 

56.  P144 Line 5. Should be “..im Mittelalter” not “..in Mittelalter”. (I can’t think what I was doing here, my only excuse being that I too am in a sort of Mittelalter.)

 

57.  P153 Line 5 should be Lincoln, Nebraska

 

58.  P153 Line 9 ‘psychotherapy’ not ‘pyschotherapy’.

 

59.  P163 Line 6. Incorrect apostrophe in ‘word’s’. Should be ‘words’.

 

60.  P165 Line -5 Should read. ‘A white bead will represent a head and a black bead will represent a tail’.

 

61.  P167 Line -8 ‘Persi Diaconis’ not ‘Persy Diaconis’.

 

62.  P172 First line. Table 9.4 should come between  ..is represented by:’ and ‘and that the process..’.

 

63.  P173 Line 16 ‘Yule’s’ not ‘Yules’s’. (Because his name was Yule not Yules.)

 

64.  P180 Line 18 ‘…six months’ service…’ not ‘…six month’s service…’.

 

65.  P182 Line 16 ‘McKendrick’ not ‘McKendrik’.

 

66.  P186 Line -5. ‘?’ not ‘.’ after ‘five years ago’.

 

67.  P189 ‘Eponymy’ not ‘Eponomy’.

 

68.  P190 Line 15. ‘multiply’ not ‘multiple’.

 

69.  P203 Line –3 “This is a ‘paradox’…” not “This a ‘paradox’…”.

 

70.  P206 Line ‘intra-uterine’ not ‘inter-uterine’. (Not so much a misprint as an inaccurate conception.)

 

71.  P207 Line-8 missing comma after ‘epidemiologist’.

 

72.  P207 Line -2 ‘meta-analyses’ not ‘meta-analyse’.

 

73.  P213 Line -11 ‘Sydney’ not ‘Sidney’.

 

74.  P219 Line 6 : ‘86% ‘not ‘86s%’.

 

75.  P219 Line 8 should be 62 000 not 62 00

 

76.  Line -1 P226 ‘Garrett Hardin’ not ‘Garret Hardin’.

 

77.  P227 Missing grave accent on ‘Molière’.

 

78.  P229 ‘Wendell Holmes’ not ‘Wendel Holmes’.

 

79.  P229 Line-3:  'golden age' not 'golden stage'. (This misprint almost works but it is a quotation from Sir David Cox and, from memory, he said ‘golden age’.)

 

80.  P231 Footnote 9 to chapter 1, p12. The correct details for the paper are: Pearson, K., Lee, A., Bramley-Moore, L. 1899.Mathematical contributions to the theory of evolution. VI. Genetic (reproductive) selection:  inheritance of fertility in man, and of fecundity in thorough-bred racehorses. Philosophical Transactions of the Royal Society Series A 192: 257-330.

 

81.  P232 Footnote 14 ‘Impostures’ not ‘Impostores’.

 

82.  P232 Footnote 18 The title of D Bernoulli’s work should be. Sur le problème propose pour la seconde fois par l’Académie Royale des Sciences de Paris’.

 

83.  P233 Footnote 27 ‘Alice’s’ (missing apostrophe).

 

84.  P233 Footnote 8 Bennett not Bennet.

 

85.  P234 Footnote 13. ‘Eponymy’ not ‘Eponomy

 

86.  P235 Footnote 20 ‘Prévision’ not ‘Prèvision’.

 

87.  P236 Footnote 7 ‘Probabilities’ not ‘Probabitities ‘.

 

88.  P236 Footnote 15 ‘measurements’ (plural).

 

89.  P239 Footnote 20. Word following ‘Chalmers’ should be ‘in’ not ‘is’.

 

90.  P240 Footnote 9 ‘Persi’ not ‘Persy’.

 

91.  P241 Footnote 13. ‘principal’ not ‘principle’.

 

92.  P242 Footnote 22. Date of Hald’s book is 1998 not 1988.

 

93.  P244 Footnote 37. Straus not Strauss.

 

94.  P245 Index. ‘Berkeley’ not ‘Berkley’.

 

95.  P245 Index ‘Breslau’ should come after ‘Brel’.

 

96.  P246 Index. ‘Diaconis, Persi’ not ‘Diaconis, Persy’.

 

97.  P246 Index ‘effectiveness’ not ‘effectivenes’.

 

98.  P246 Index ‘Gelert and Llewelyn’ not ‘Gelert and Llewlyn’.

 

99.  P247 Index. ‘Hardin, Garrett’ not ‘Hardin, Garret’.

 

100.                    P249 Index under ‘randomization’ should be ‘auxiliary’ not ‘auxilliary’.

 

101.                    P250 Index ‘Sydney’ not ‘Sidney’.

 

102.                    P250 Index ‘Eponymy’ not ‘Eponomy’ (Again! Perhaps we are in need of a Senn’s Law of Mispsellings?)

 

103.                    P250 Index Under ‘Student’ should be ‘Gosset’ not ‘Gossett’.

 

104.                    P250 Index. P250 No comma after ‘Tatie’.

 

105.                    P251 Index ‘Whittaker’ not ‘Whitaker’.

 

106.                    P251 Index Missing comma after ‘Witt’.

 

107.                    P251 Index Under ‘Wright’ should be ‘Sewall’ not ‘Sewell’.

 

 

Errors in reprinting

 

None of the above errors, alas, was corrected in reprinting. However, two further ones were added to the back cover

 

  1. The correct quotation from Biometrics would have had in the first line, ‘…been really…’ rather than ‘…really been…’

 

  1. In quotation from Deborah Ashby in the British Medical Journal, first line, it should read, ‘…to do for medical statistics…’

 

Return to Dicing with Death main page.

 

Let me know of some other ghastly mistake: stephen@senns.demon.co.uk

 

 

This page last amended 8 August 2007.