Suppose the letters $a, \,b, \,c, \,d, \,e, \,f$ have probabilities $\dfrac{1}{2}, \dfrac{1}{4}, \dfrac{1}{8}, \dfrac{1}{16}, \dfrac{1}{32}, \dfrac{1}{32}$, respectively.
What is the average length of the Huffman code for the letters $a, \,b, \,c, \,d, \,e, \,f$?
- $3$
- $2.1875$
- $2.25$
- $1.9375$