Accuracy of a random classifier. A particular data set has $4$ possible labels, with the following frequencies:

Label Frequency

A $50\%$

B $20\%$

C $20\%$

D $10\%$

$($a$)$ What is the error rate of a classifier that picks a label $($A$,$B$,$C$,$D$)$ at random, each with probability

$1/4?$

$($b$)$ One very simple type of classifier just returns the same label, always.

$$ What label should it return?

$$ What will its error rate be$?$