$[3\mathrm{.}8/20$ Points$]$

DEIAILS

$($State $1)$ and a $0\mathrm{.}5$ probability that the customer shopped at Catalina's $($State $2)$ at period $0$ ; that $is,{}_1(0)=0\mathrm{.}5$ and ${}_2(0)=0\mathrm{.}5.$

Given these initial state probabilities, develop a table showing the probability of each state in future periods. $($Round your answers to three decimal places.$)$

$\backslash$table$[[,\backslash$table$[[$State$],[$Probability$]]],[,{}_1(n),{}_2(n)$