Tue 4 May 2010
A modest puzzle on probabilities
Posted by Happy under Fun, puzzle
Comments Off on A modest puzzle on probabilities
Two witnesses provided evidence in court.
Tom is a somewhat reliable witness giving accurate testimony 70% of the time. Harry is less reliable, giving accurate testimony 60% of the time.
Both testified to the same effect.
What is the chance that their evidence was indeed accurate ?
Think carefully now.
[Thanks to Mark W for this one.]
Answer: 77.8%
Rational: If these witnesses testified multiple times, they would be:
Both wrong: 12%
Both right: 42%
Tom right, Harry wrong: 28%
Harry right, Tom wrong: 18%
In this instance they agree, so only the first two cases apply. The probability they are both right is 42/(42+12) = 7/9 = 77.8%.
You should be able to get there using Bayes theorem, but I find this approach easier.