Consider a four$-$year program. Suppose the probability of leaving $($forever$)$ after Year $1$ is $14\%,$ after Year $2$ is $8\%,$ and after Year $3$ is $3\%.$ The probability of repeating any year is $5\%.$

Based on this description, fill in the missing entries for the transition matrix below. $($Assume there are no other possibilities, like skipping a year, leaving and coming back, etc.$)$

$($from$)$ Year $1$: Year $2$: Year $3$: Year $4$: Graduation: Left program: $($to$)$ Year $1$: Answer $1$ Question $3$

Answer $2$ Question $3$Answer $3$ Question $3$Answer $4$ Question $3$

$00$Year $2$: Answer $5$ Question $3$

Answer $6$ Question $3$Answer $7$ Question $3$Answer $8$ Question $3$

$00$ Year $3$: Answer $9$ Question $3$

Answer $10$ Question $3$Answer $11$ Question $3$Answer $12$ Question $3$

$00$ Year $4$: Answer $13$ Question $3$

Answer $14$ Question $3$Answer $15$ Question $3$Answer $16$ Question $3$

$00$ Graduation: Answer $17$ Question $3$

Answer $18$ Question $3$Answer $19$ Question $3$Answer $20$ Question $3$

$10$ Left program: Answer $21$ Question $3$

Answer $22$ Question $3$Answer $23$ Question $3$Answer $24$ Question $3$

$01$

What is the probability $($as a decimal between $0$ and $1)$ that a typical student graduates from the program after the expected four years? Answer $25$ Question $3$

Suppose there are currently $800$ Year $1$ students, $600$ Year $2$ students, $720$ Year $3$ students, and $620$ Year $4$ students. To the nearest whole number, how many students are expected to have graduated within the next four years? Answer $26$ Question $3$