Probability: The Basics
Birthday Problem (Modified)
There are 100 people in a room. Assume each person’s birthday is equally likely to be any of the 365 days of the year (no leap babies) and birthdays are independent. What is the probability that at least three of them share the same birthday?
Use simulation to answer this question. You need to explain your code so we can assess whether you have got the idea of using random samples and loops to simulate the estimated probability.
The Monty Hall Game
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?
Use simulation to answer this question. You need to explain your code so we can assess whether you have got the idea of using random samples and loops to simulate the estimated probability.