Activity: simulation

Instructions:

• Work with a neighbor to answer the following questions
• To get started, download the class activity template file
• When you are finished, render the file as an HTML and submit the HTML to Canvas (let me know if you encounter any problems)

Probability simulation: 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

1. Create a vector to store the days of the year (numbered 1 to 365)

2. Use the sample function to randomly choose birthdays for the class (think about whether we want to sample with or without replacement here…)

3. 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?

4. Use a for loop to repeat the experiment nsim=10000 times, making sure to store the results. What is the probability of at least one shared birthday?

5. How many students do we need for the probability to be approximately 50%?