Extra Bits Per Token

A tagger sorts every token of a corpus into one of three buckets: noun, verb, other. Counting over the whole corpus gives the true distribution

$P = [\,0.7,\ 0.2,\ 0.1\,]$

A crude baseline model, which never looks at context, always predicts

$Q = [\,0.5,\ 0.25,\ 0.25\,]$

You want to know how many extra bits per token this baseline wastes compared with a coder that knew $P$ exactly — that is, the KL divergence $D_{KL}(P \parallel Q)$ measured in bits.

Base-2 logarithms (you will not need all of them):

What is $D_{KL}(P \parallel Q)$, in bits? Round your answer to 3 decimal places.