$8-23)$ Assume $i=\mathrm{.}08$ and that we are dealing with a four$-$year seleat

period. We know that $q_{[30]}=\mathrm{.}40,p_{[30]+1}=\mathrm{.}80,q_{[30]+2}=\mathrm{.}10$ and

$q[30]+3=\mathrm{.}10.$ Also $D_{34}=1000$ and $D_{35}=920.$ Find the probabj.

lity that a person entering the select group at age $30($a$)$ will

remain in the population for $5$ years; $($b$)$ will remain in the

population for at most $3$ years.