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Tangled Words and Messages

Consider these two statements:

  1. The percentage of men who are doctors
  2. The percentage of men among doctors
Are they saying the same thing? Explain.


Source: Variation of M.S. Numeracy discussion listserve, Aug 8, 2006

Hint: Try to draw a Venn Diagram to represent the two situations.


Solution Commentary: Using conditional probability notation, Statement (1) is saying Prob(Doctor|Man) while Statement (2) is saying Prob(Man|Doctor). Thus, they are not saying the same thing.

For more of this vocabulary exercise, consider the two sentences:

  1. Widows are more likely among suicides than widowers.
  2. Widows are more likely to commit suicide than widowers.
Now, are they saying the same thing? Explain.