Class Activity, August 28

Instruction: Work with a neighbor to answer the following questions. Solutions will be posted on the course website. To get started, download the class activity template file.

The birthday problem

Suppose we have a class of 30 students. What is the probability that there is at least one shared birthday?

Assume there are 365 days in a year
Assume that each day is equally likely as a birthday
Assume there are no multiple-birth siblings (e.g. twins, triplets, etc.) in the class

Create a vector, days, to store the days of the year (numbered 1 to 365)
Use the sample function to randomly choose birthdays for the class (shared birthdays are possible, so use replace=TRUE in the function!)
Check the number of distinct birthdays (hints: unique returns the unique elements of a vector; length returns the length of a vector). Are there 30 distinct birthdays?
Use a for loop to repeat the experiment \(n_{sim} = 10000\) times, making sure to store the results. What is the probability of at least one shared birthday?
Repeat the simulation with different class sizes. How many students do we need for the probability of a shared birthday to be approximately 50%?