*Let G be the event that a certain individual is guilty of a certain robbery. In gathering evidence, it is learned that an event $E\_1$ occurred, and a little later it is also learned that another event $E\_2$ also occurred.
Is it possible that individually, these pieces of evidence increase the chance of guilt (so $P(G|E1)$ $> P(G)$ and $P(G|E2) > P(G)$), but together they decrease the chance of guilt (so $P(G|E1, E2)$ $ < P(G)$)?*

This is the example in the solution:

> 
> Suppose that the crime was
> committed between 1 pm and 3 pm on a certain day. Let E1 be the event
> that the suspect was at a nearby coffeeshop from 1 pm to 2 pm that
> day, and let E2 be the event that the suspect was at the nearby
> coffeeshop from 2 pm to 3 pm that day. Then P(G|E1) > P(G), P(G|E2) >
> P(G) (assuming that being in the vicinity helps show that the suspect had the opportunity to commit the crime), yet
> P(G|E1, E2) < P(G) (as being in the coffeeshop from 1 pm to 3 pm gives
> the suspect an alibi for the full time).
> 
> 
> 

I've been trying to think of another example but I can't think of any. Can someone provide another example? Moreover, in terms of general problem-solving heuristics, I find myself *terrible* at coming up with examples/counter-examples. My only strategy is to look for simple/extreme cases, but there's no simple/extreme cases for this question.

Thank you very much!