the trees in a Random Forest What I want to ask is as follows:


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*Is it possible that there are many identical trees in a Random Forest?

*If there was very little different training data in a tree sample by bootstrap aggregating, do we need to discard the tree?
 A: There are several reasons why a random forest could have multiple identical trees. However, if you have an a moderate amount of data about a relation that is not trivial this is not likely to occur. 
To answer you question. If you have a small number of variables and/or records than random forest might sample the same variables and/or records multiple time by coincidence. However, since the number of possible combinations of variables and records increases rapidly the probability of this happening decreases rapidly when the size of the data increases. 
A second possibility is that the relation you are trying to model is trivial. For example, only one predictor is needed to grasp the relation. Then each time the predictor is included into the selection of variables the resulting tree is the same. But then, why would you use random forests...
The second question is only relevant if very few use-cases because it would only occur with very few records (e.g. < 50). In these cases you can better use other learning techniques. If you do use random forests, learning a tree on a trivial subset (all the same record) might result in a tree that generalizes very badly but it also might highlight a very specific relation in your data. Consequently, there is no general rule about if you want to keep this tree. But as said, you better use other learning techniques. 
