The university has a student population of $15,000,$ with $15\%$ of them retaking the introductory statistics $($STAT$)$ course. During the summer session, an instructor teaching the introductory STAT course is interested to know a$.$ What is the probability that at least $19$ out of the $105$ students in her class were repeating the course? b$.$ What is the probability that at most $19$ out of the $105$ students in her class were repeating the course.