Besides this problem I also use the following one to rise the interest of my students on the Probabilities Theory. It's a funny puzzle were the use of simple arithmetic rules doesn't work. We have to workaround a little bit to find the answer.
So here it goes:
The Random Family decided to go on a picnic next Sunday.
So they tried to get some information about the weather and predict if it will be a sunny Sunday.
They went online to weatheronsundays.org and happily saw that Sunday most likely be sunny (the algorithm used on this site forecasts correctly the weather about four in five times).
The youngest daughter also went to the CheckTheWeatherOnNextSundaySoYourFamilyPicnicWillBeASucess application on her smart phone and also saw that next Sunday will be sunny (this application forecasts correctly about three times out of four).
Based on this two predictions, what is the probability of the next Sunday will be sunny?