Conditional Probability - Basic Question On question 2b. below, why does knowing the extra bit of information A increase the probability of D?


From the question I get the feeling that you want an answer regarding intuition and not so much mathematics. If I'm wrong, please comment and I will change my answer. 
From the probabilities given, we see that it is much more likely that the whole shipment consists of forgeries (10%) than it is likely that only 2,3 or 4 paintings are forgeries (2%, 1% and 2%). Hence, knowing that there is at least 1 forgery in the shipment, increases the chance that the whole shipment is "tainted".
