Question

We have seen in lectures that if 50 people are chosen at random then there is a 97% chance that at least two of them share the same birthday. Use similar calculations to answer the questions below. Assume that an ANU student is equally likely to have any one of 000 ... 999 as the last three digits of their ID number.

(a) What is the percentage chance that in a working group of five students at least two have the same last digit of their ID?

(b) What is the percentage chance that from a course with an enrolment of 100 students at least two have the same last three digits of their ID?
NB: If your calculator cannot handle the large numbers involved, you could use WolframAlpha (www.wolframalpha.com) or some other on-line tool.

(c) By experimenting using WolframAlpha, or otherwise, find the minimum number N for which there is a better than even chance that from N randomly chosen students at least two have the same last three digits of their ID. As a start, try N = 40.

Answer 1

The theoretical probabilities are as given below.

The probability that numbers such that do not match is given by

So the probability that at least 2 of randomly selected people share the same 3 digits is

a) When , the required probability is

b)When , the required probability is

c)

We have for ,

We have for ,

Thus the required minimum number is ​​​​​​​