Editing Statistics and Statistical Programming (Winter 2021)/Problem set 5 (section)

===SQ2. Birthdays revisited (Optional bonus!)===

'''Optional bonus statistical question'''

You did a question about birthdays in the context of one of the textbook exercises for ''OpenIntro'' Chapter 3. Here's an opportunity to apply your knowledge and extend that exercise. Note that you can absolutely use R to help calculate the solutions to both parts of this problem. That said, it's a super famous problem and answers/examples are all over the internet, so if you want to challenge yourself, don't look at them while you're working on it! The only hint I'll give you is that you may find [https://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficients] useful and the <code>choose()</code>) function can calculate them for you in R.

# Imagine that there were 25 people in this class and that I offered you a choice between two bets: Bet #1 is determined by the flip of a fair coin. You can choose heads or tails and you win the bet if your choice turns out to be correct). Bet #2 is determined by whether any two members of that previous version of the class shared a birthday. If a birthday was shared I win the bet, and if no shared birthdays were shared you win the bet. Assuming you want the best chance of winning, which bet should you choose?
# Now calculate the probability that any two members of our 5 person class share a birthday and compare this probability with the results of SQ2.1 above.