Flipping the labels in a classification problem

Question

Let us say A- we have a binary classifier with labels 1 as healthy and 0 as sick. The precision we got is 100% and the recall is 70%.

Now let us say B-we flip the labels where 0 is healthy and 1 as sick.

Are Precision and recall get flipped in their values if you flip the labels? So in the new case, recall is 100% and precision is 70%?

Or the (70,100) values in the first case belonged to class 1 aka, healthy people and I should calculate the precision and recall for class 0?

My understanding was that we were able to recall 70% of sick people and out of every people who we detected as sick, no person was healthy (precision as 100%). But I am confused now

Answer 1

To begin with, I don't quite get it why you want to flip them. In the binary case, you flip Negatives and Positive, so True Negative becomes True Positive and so do FP/FN. Hence you flip specificity/true negative and sensitivity/recall values, so overall accuracy and F1 stay the same.