Question

4. For the following problem, ignore the year of birth while comparing two birthdays. Moreover, assume that the year is exactly 365 days (ignore the 29th of February) Note that matching birthdays means the birthdays are the same (a) You are a member of a class room that has n 1 students including you. What is the probability that you find at least one student, other than you, who has a birthday that matches yours? (b) In another classroom that has m students (m << 365), what is the probability that at least two students have matching birthdays? (c) Now let Pi be the probability that you do not find any student, in your classroom that has n +1 students, who has a birthday that matches yours. Additionally, let P2 be the probability that there are no birthday matches in the room that has m students (m << 365). Derive the relation between n and m such that P P2 Hint: The following approximation will be useful: for small x, 1-e.

Answer 1