write me a problem statement with answer on evaluation recall rate

Problem Statement:

In a recent information retrieval system evaluation, a system returned 200 relevant documents out of which only 150 were truly relevant. The total number of relevant documents in the database is 300. The task is to evaluate the recall rate of the system.

Solution:

Recall rate is a measure of the completeness of a system. It is the number of relevant items retrieved by a search divided by the total number of existing relevant items.

In this case, the number of truly relevant documents retrieved is 150 and the total number of relevant documents in the database is 300.

So, the recall rate can be calculated as follows:

Recall Rate = (Number of truly relevant documents retrieved / Total number of relevant documents) * 100%

Substituting the given values:

Recall Rate = (150 / 300) * 100% = 50%

Therefore, the recall rate of the system is 50%.