Meaningful answers

Which drink tastes better - Coca-Cola or Pepsi? In a recent focus-group discussion, a market research company asked this question to a 100 people and of them, 90 said Coca-Cola while 10 said Pepsi. To further understand if people are able to distinguish between the two drinks on the basis of it's taste, the agency asked 5 volunteers from the "i-love-pepsi" group to sip 5 bottles of the blank-labeled cold drinks presented to them, and tell us the right drink. Amazingly in 4 out of five occasions they got it right.

Conclusion : 80% of all people are able to identify the taste of the drink they are having and 90% say Coca-Cola is better.

Let's revisit this - 0.8 is the probability of a person identifying the right drink which means he/she has a 0.2 probability of doing the opposite (reading the wrong drink). Which means, of the 90 Coca-Cola afficionades, it's possible that 20% of them would have got their taste wrong i.e. although they say "I-love-Coke", they would have selected Pepsi from the draw. Simialrly, the Pepsi group of 10 would have 2 people who would have tasted a Coca-Cola as the superior taste. So we have 16 "CC to P" people and 8 "P to P" people = 24 "I-love-Pepsi" people

Or, not 90% of the people love Coca-Cola but only 76%. And Pepsi goes up from 10% to 24%. Consequently, the probability of a Pepsi lover choosing a Pepsi from two drinks after sipping it, is only 8/24 = 0.33