An interesting problem from probability is the birthday problem. The problem deals with determining the likelihood that at least two people share the same birthday in a room of n individuals. The data file 5_6_1 located at www.pearsonhighered.com/sullivanstats represents simulated birthdates of 15 individuals 2000 times. Each birthdate was assigned a number from 1 (January 1) to 365 (December 31).
(a) What is the birthdate of the randomly selected individual in row 1, column 1? Did the first simulation result in at least two people sharing the same birthdate?
(b) Based on the simulation, what is the probability that at least two people will share the same birthdate?
(c) Use the Birthday problem applet in StatCrunch to simulate randomly selecting 15 individuals. Repeat the simulation at least 2000 times and determine the proportion of samples that result in at least one common birthday.