The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities.

$\backslash$table$[[,$To$],[$From$,$Special B$,$MDA$],[$Special B$,0\mathrm{.}90,0\mathrm{.}10],[$MDA$,0\mathrm{.}02,0\mathrm{.}98]]$

$($a$)$ Which brand appears to have the most loyal customers? Explain.

$--$Select$--$ ~~ has the most loyal customers because $\%$ stay with them and only $\%$ switch to the other brand, as opposed to where only $\%$ stay with them and $\%$ switch.

$($b$)$ What are the projected market shares for the two brands? $($Enter exact numbers as integers, fractions, or decimals.$)$

Special B $,{}_1=$

MDA $,{}_2=$