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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 in the 1st edition

 

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(A│B)

 

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.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 Moli re .

 

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 probl me propose pour la seconde fois par l Acad mie 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 Pr vision not Pr vision .

 

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'

Errors in the 2nd Edition

I am grateful to Paul Krause, who is the first to point one out to me.
1. P69 Figure 3.1. I have plotted squares where I meant to plot circles and vice versa. This was correct in the first edition.

 

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

 

 

This page last amended 20 March 2024.