The Pigeonhole Principle suggests that where there are 367 people, at least two people must share the same birthday. Research the principles of the Birthday Problem, and

use these principles to:

1. Show that the number of people randomly chosen is significantly less than that

suggested by the Pigeonhole Principle. [3]

1. Find the smallest number of people you need to choose at random so that the

probability that at least two of them share the same birthday, is in excess of

95% [3]

1. State any assumptions made for parts i. and ii. [1]