A classifier is being tested on two datasets: Dataset $1,$ with $100$ positives and $100$ negatives, and Dataset $2,$ with $100$ positives and $500$ negatives. The confusion matrices of the classifier on the two datasets are provided below. Dataset $1$ Predicted $+$ Predicted $-$ Actual $+8020$ Actual $-2080$ Dataset $2$ Predicted $+$ Predicted $-$ Actual $+8020$ Actual $-100400$ a$)$ Calculate the Precision, Recall, TPR$,$ and FPR for the classifier on Dataset $1$ and Dataset $2.$ b$)$ Based on your observations from these results, if you had to choose between the following two evaluation metric pairs: $\{$precision$,$ recall$\}$ and $\{$TPR$,$ FPR$\},$ which one would you choose in the following scenarios and why? Provide brief explanations in context with your observations from the results above. The evaluation is required to be invariant to changes in the relative numbers of positives and negatives in the evaluation dataset. c$)$ Compute the accuracy of the classifier on Dataset $2($you can leave your answer in fractions$).$ Construct a trivial classifier that can achieve better accuracy on Dataset $2$ without even looking at the attributes of the data. What is the accuracy of this trivial classifier?