Introduction to Cryptography with Coding Theory, 3rd Edition

B.9 Examples for Chapter 12

Example 36

Suppose there are 23 people in a room. What is the probability that at least two have the same birthday?

SOLUTION

The probability that no two have the same birthday is $\prod _{i=1}^{22}(1-i/365)$ (note that the product stops at $i=22\text{,}$ not $i=23$). Subtracting from 1 gives the probability that at least two have the same birthday:

> 1-mul(1.-i/365, i=1..22)

                                .5072972344

Note that we used $1.$ in the product instead of 1 without the decimal point. If we had omitted the decimal point, the product would have been evaluated as a rational number (try it, you’ll see).

Example 37

Suppose a lazy phone company employee assigns telephone numbers by choosing random seven-digit numbers. In a town with 10,000 phones, what is the ...