Answer:
[tex]\frac{{13 \choose 9}}{{18 \choose 9}} [/tex]
Step-by-step explanation:
The student will answer correctly the quiz if he/she knows the answer to all of the quiz problems. The quiz consists of 9 problems out of the set of 18 problems. That means the professor could create [tex]{18 \choose 9}[/tex] different quizzes (which are the ways to choose a group of 9 problems out of the 18 problems). The student however doesn't know the answer to all of those different quizzes. He/she only knows the answer to the quiz if the 9 problems are all taken from the 13 problems he/she has already figured out. The number of quizzes that could be created, taking all 9 problems from the 13 problems he/she has already figure out is [tex]{13 \choose 9}[/tex]. So, the student is only able to answer [tex]{13 \choose 9}[/tex] of all possible quizzes the professor could come up with. Therefore the probability that the student answers correctly the quiz is [tex]\frac{{13 \choose 9}}{{18 \choose 9}} [/tex]
