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 $0\mathrm{.}020\mathrm{.}98$

$($a$)$

Which brand appears to have the most loyal customers? Explain.

Correct: Your answer is correct.

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

Correct: Your answer is correct.

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 $2=$