Chapter 9.5, Problem 7QE

Explanation of Solution

Find minimum number of people in a group so that at least two people in group have same birthday and relate this problem to file structures:

The numbers of people will be associated with some probability. We will find the number of people for a probability of just more than $0.5$.

The probability can be easily calculated by first calculating the probability for not having the same birthday.

Calculating for $23$ people

Probability of not having same birthday is,

$\begin{array}{c}P\left(A\text{'}\right)=\frac{365}{365}\times \frac{364}{365}\times \frac{363}{365}\times \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \cdot \times \frac{343}{365}\\ \approx 0.493\end{array}$

Here,

• $P\left(A\text{'}\right)$ is the probability of not having same birthday