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.