15) Sampling

Sampling is a process of selecting a subset of individuals or items from a larger population to make inferences about the population. 
Two common methods of sampling are:

1. Sampling with Replacement (random.choices()):
   - In this method, each item in the population can be selected more than once in the sample.
   - It is useful when you want to allow the same item to be selected multiple times in a sample.
   - For example, if you are simulating a scenario where you draw a card from a deck, replace it, and draw again, you would use sampling with replacement.

2. Sampling without Replacement (random.sample()):
   - In this method, once an item is selected in the sample, it is not available for selection again.
   - It is useful when you want to ensure that each item is selected only once in the sample.
   - For example, if you are selecting students for a survey and you want to ensure that each student is selected only once, you would use sampling without replacement.

The formula you provided is for estimating the number of desired outcomes (x) in a population (N) based on a sample (n) where x out of n samples are the desired outcome. 
This formula assumes that the sample is representative of the population and can be used to estimate the total number of desired outcomes in the population.

In your example, if you have a population of 50 and you draw a sample of 13 where 8 samples are the desired outcome, you can estimate the total number of desired outcomes in the population as N*(x/n). 
So, in this case, it would be: 50*(8/13).