Let's try some school math first: If everyone had been at Donald´s, we would have expected five wins. If they had all been at Gustav´s, we would have expected 20 wins. Now our result is in between with 16 wins. A little bit lazy we guess: There were 50 persons at Donald´s and 50 persons at Gustav. That would lead to the following expectation of wins:
50*5% + 50*20% = 12.5
This is still a little smaller than our observed 16. Presumably, therefore, a little more than half of the people were at Gustav´s. With some school mathematics we can save the trying and calculate explicitly: If x persons were at Gustav´s, we have the following expectation about the number of wins:
(100 – x)*5% + x*20% = 5 + x*15%
Setting this equal to the observed 16 wins, we get for x:
5 + x*15% = 16
x = 11/0,15 = 73.33
This is also called the maximum likelihood estimator. The result says that the most plausible explanation for our 16 observed wins is when about 73 people were at Gustav´s and 27 people were at Donald´s. So far, so plausible. So let's prepare the press release »Most people buy lottery tickets at Gustav's«.