Accuracy of a probability estimate How can you classify the accuracy of a probability?
Say I do a study of people that like bananas in 2 different regions.

*

*Region 1: 8 out of 10 people tested like bananas.

*Region 2: 500 out of 1000 people tested like bananas.

So in region 1, 80% of people like bananas. In region 2, 50% of people like bananas. I have a dilemma if want to sell bananas in either region 1 or 2. The accuracy of the probability in region 1 will be worse than in region 2. How can I quantify this accuracy to make a decision, in which region should I sell bananas?
 A: This sounds like this question could be rephrased as "Is the proportion of people who like bananas in Region 1 significantly different than in Region 2?"
Reframed that way, the statistical test would be for the z-test for the difference between two proportions. 
Here is a link to an online calculator: http://epitools.ausvet.com.au/content.php?page=z-test-2
Note, however, that Region 1 (at least in your example), is undersampled, and the statistical tests may be inaccurate. Many sources recommend sampling until you have at least 10 people who meet each condition (in this example, 10 people who like and 10 who dislike bananas in each region). 
A: my experience
Use GraphPad (for example) and get the p-value for 
                        8   2
                      500   500

You will p=0.1077 not significant at 5%.
Try the same proportion for region 1 (80%) this time with 20 oservations
                       16   4
                      500   500

Surprised?
A: In this particular case, accuracy/precision and other sensible considerations don't matter. If the information that you gave in the question is all you know, then you have to sell bananas in region 1. Period.
However, if the price of bananas in region 2 was higher than in region 1, it would have been a different story. The reason is that the price asymmetry would bring the cost of error asymmetry. 
What if in reality the region 2 liked bananas more than region 1? In this case although given the data it seems that region 1 has higher propensity to buy bananas, depending on the price differential the cost of error could be too high given the variances of your estimates.
UPDATE:
@whuber brought up an interesting topic: risk aversion. If you're averse to risks, then you may consider expected utility theory, it's studied in microeconomics and game theory. The trouble is that there's not enough data to set up the expected utility function. 
For instance, in finance the simple examples are usually like follows. You have two stocks. Stock 1 returns 80% annually with standard deviation 60%, Stock 2 returns 50% annually with standard deviation 5%. Which stock to choose?
You need a utility function, such as $U(\mu,\sigma)=\mu-\sigma^2$. In this case $U_1=44%$ and $U_2=0.4975$., so you have to go with the Stock 2 despite its average return us lower, because it's risk is "too high". 
