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

To

From Special B MDA

Special B $0\mathrm{.}900\mathrm{.}10$

MDA $0\mathrm{.}040\mathrm{.}96$

$($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

$---$Select$---$

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 $2=$