How to predict a group of events using machine learning?
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Assumptions before answering your question:


The Target variable is a categorical(each stage is considered as a separate category).
You have the past data of the customers whose application got rejected(if hasn't reached the last stage)/successful(reach last stage) at the respective level. For Example, customer A applied and got his application rejected at stage-2, No Legal). 
You have some demographics of the customer to predict the stage at which the application might get rejected. 
You have good data(no outliers, well engineered features, good understanding on data etc).


Now if the above assumptions are met, then you can apply Machine Learning algorithms which are used for doing multi-class classification.

Applicable Algorithms:


Neural Networks
Random Forest
K nearest Neighbor
Decision Tress
Support Vector Machines etc.


Finally, you can apply Ensemble model by combining results of the 2 or more models.

For measuring the accuracy you can use Confusion Matrix(By diving the data into Test: 30% of data and Train: 70% of data).