Tangled Words and Messages
Consider these two statements:
Are they saying the same thing? Explain.
- The percentage of men who are doctors
- The percentage of men among doctors
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:
Now, are they saying the same thing? Explain.
- Widows are more likely among suicides than widowers.
- Widows are more likely to commit suicide than widowers.