Question

. Consider your class of 29 students. Calculate the probability that at least two students have the same birthday. For this purpose, assume each day of the year is represented by a box, and we place the name of the student in the box corresponding to their birthday. (a) List total number of possible arrangements. (b) List total number of arrangements that do not have two names in the same box. Obtain the probability that no two students have the same birthday. (c) Finally, obtain the probability that at least two students have the same birthday.

Answer 1

a)total number of possible arrangements =N(for each student name has 365 choice of boxes)=365²⁹

b) number of ways that a box contains at most 1 name =N(first name has 365 ; second name has 364 ; ...and 29 th name has (365-29+1)=365*364*.....*337=6.46*10⁷³

c)therefore at least two have same birthday =1-P(none have same birthday )

=1-6.46*10⁷³/365²⁹ =0.6810