Consider a matrix $M\times T$, where $M=5$ and $T=4$.
For each $m=1,...,5$ and $t=1,...,4$, the $(m,t)$-th entry of the matrix is a letter among $a,b,c,d$.
Let us denote by $X_{m,t}$ the $(m,t)$-th entry of the matrix.
Let us define $$ p_{a}\equiv \frac{1}{5} \ \times \Big|\Big\{m\in \{1,...,5\}: X_{m,t}=a \text{ for some } t\in \{1,...,4\} \Big\}\Big| $$ Define similarly $p_b, p_c, p_d$.
For example, based on the example matrix below, $p_a=1, p_b=3/5, p_c=3/5, p_d=2/5$.
Observe that $p_a,p_b,p_c,p_d$ are all between 0 and 1.
Question: can we characterise where $p_{a}+p_b+p_c+p_d$ lies? For example, we cannot have that $p_a=0.2, p_b=0, p_c=0, p_d=0$. Also, I think $p_{a}+p_b+p_c+p_d\geq 1$.
PS: please feel free to change/suggest tags, I'm not sure which one is the right one.