This is an extension of the Birthday Problem. Suppose you have500 Facebook friends. Make the same assumptions here as in theBirthday Problem.
a) Write a program in R to estimate the probability that, on atleast 1 day during the year, Facebooks tells you three (or more) ofyour friends shat that birthday. Based on your answer, should yoube surprised by this occurrence?
b) Write a program in R to estimate the probability that, on atleast 1 day during the year, Facebook tells you five (or more) ofyour friends share that birthday. Based on your answer, should yoube surprised by the occurrence? [Hint: Generate 500 birthdays withreplacement, then determine whether any birthday occurs three ormore times (five or more for part (b)). The table function in R mayprove useful.]
