Activity: Intro to Python

Instructions:

• Work with a neighbor to answer the following questions
• You do not need to submit anything for this activity

Working in Python: To work in Python, you will connect to the DEAC OnDemand server:

https://sta279-f25.github.io/resources/rstudio_server/

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

In a previous class activity, we wrote the following R code:

days <- 1:365 # days of the year
n_students <- 30

nsim <- 10000
results <- rep(NA, nsim) # store the simulation results
for(i in 1:nsim){
  birthdays <- sample(days, n_students, replace=TRUE)
  results[i] <- length(unique(birthdays)) < n_students
}

mean(results)

In this class activity, we will re-write the code in Python.

1. Use the np.arange function to create a 1-dimensional array, days, to store the days of the year (numbered 0 to 364)

2. Use the np.random.choice function to randomly choose birthdays for the class (shared birthdays are possible, so use replace=True in the function!)

3. Check the number of distinct birthdays (hints: the np.unique and len functions may be helpful!). 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?