I want to calculate the Entropy of the phrase "Eile mit Weile". I found the probability of each letter as the following
$$P(e)=\frac{4}{12}$$ $$P(i)=\frac{3}{12}$$ $$P(l)=\frac{2}{12}$$ $$P(m)=\frac{1}{12}$$ $$P(t)=\frac{1}{12}$$ $$P(w)=\frac{1}{12}$$
Then I used the formula for entropy $$H(p_1,...,p_k)=-\sum_{i=1}^{k}p_i\log_2(p_i)$$ $$H(p_1,...,p_k)=-(\frac{4}{12}\log_2(\frac{4}{12})+\frac{3}{12}\log_2(\frac{3}{12})+\frac{2}{12}\log_2(\frac{2}{12})+\frac{1}{12}\log_2(\frac{1}{12})+\frac{1}{12}\log_2(\frac{1}{12})+\frac{1}{12}\log_2(\frac{1}{12}))≈2.355388542 \ Bits$$ But the correct answer is $1.63263$ Bits. I've made a mistake somewhere but can't figure out what I did wrong.