Colourblindness and probability

A female acquaintance of mine was recently surprised to find that both of her sons were colourblind, despite neither parent being colourblind. A natural question to ask is ‘What are the odds?’ This question turns out to be open to interpretation, depending on what we mean by probability and odds.

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Primary, secondary and ternary sources

I am a bit annoyed that scientists don’t always seem to get the difference between primary, secondary and tertiary sources. Consider this situation:

  • Prince (2008) reports that pigs are approximately blue.
  • Quail (2006), Quaffer (2008) and Qi (2009) use the approximation that pigs are blue.
  • Rout (2012) is a review article discussing the aforementioned works.

Which of the following are valid?

  1. ‘Pigs are approximately blue (Prince 2008).’
  2. ‘Pigs are approximately blue (Quail 2006, Quaffer 2008, Qi 2009).’
  3. ‘We use the approximation that pigs are blue (Prince 2008).’
  4. ‘We use the approximation that pigs are blue (Quail 2006, Quaffer 2008, Qi 2009).’
  5. ‘We use the widely-used approximation that pigs are blue (Quail 2006, Quaffer 2008, Qi 2009).’
  6. ‘We use the widely-used approximation that pigs are blue (Rout 2012).’
  7. ‘The approximation that pigs are blue is widely used (Quail 2006, Quaffer 2008, Qi 2009).’
  8. ‘The approximation that pigs are blue is widely used (Rout 2012).’
  9. ‘Many authors, including Quail (2006), Quaffer (2008) and Qi (2009), use the approximation that pigs are blue.’
  10. ‘Many authors, including Quail (2006), Quaffer (2008) and Qi (2009), use the approximation that pigs are blue (Rout 2012).’