Question: 2015 Fall Final - 16

You are given that:

• The course COMP 9999 runs over a period of one year, starting on January 1 and ending on December 31. There is one lecture every day; thus, the total number of lectures is 365.
• Dania and Nick take this course. Dania's birthday is on November 19. Nick's birthday is on December 3.
• Professor G. Ruesome teaches the course. Professor Ruesome decides to have 20 quizzes during the year. For this, he chooses a uniformly random subset of 20 days; the quizzes will be on the 20 chosen days. (It is possible that there is a quiz on January 1.)

Determine the conditional probability $\Pr(B|C)$, where $B$ and $C$ are the events

• B = "there is a quiz on Nick's birthday",
• C = "there are exactly 5 quizzes in December".