Computer Science class
Probability of Collision
In the University of Asguard, every student can design their own student ID. Here is the rules for getting the student ID:
1. The first character should be an upper-case English letter. Students can pick any letter except letter ”F”, which is reserved for faculties and staff.
2. The following two digits should be the month of student’s birthday.
3. The last four characters are 4 digits chosen by each student.
For example, Z051133 is an valid ID for a student who was born in May. We assume that each student will randomly choose the first English letter and the four digits. In a Computer Science class, the instructor tells the class that there is at least a 50% possibility that two or more students share the same first four characters in their student ID.
(a) At least how many students are there in the class? Explain your solution. (Assume that the distribution of the birth months is uniform.)
(b) One student says that the first four characters are ’A019’ and asks his classmates to raise the hand if someone has the same first four characters. However, no one responds. Has the instructor made a mistake?
Hint: Think about relevant properties of hash functions and contrast the instructor’s logic and the student’s question.