Question

Suppose you consider your birth date to be special since it falls on October31and the class you are in has 29 students.

a. Is the probability of finding at least one student with a birthday that matches yours greater​ than, the same​ as, or less than the probability that there is at least one birthday match in your class ​(0.681​)?

b. Find the probability that at least one other student in the class has your birthday.

The probability that at least one other student has your birthday is approximately___

Answer 1

a)here as having at least one match with your birthday is an specific case of at least one birthday match in class ; therefore it is less probable  than the probability that there is at least one birthday match in your class ​.

P(at least one birthday match in class) =1-P(none have same birthday)

=1-(choosing 29 different days out of 365) =1-(³⁶⁵P₂₉)/(365)²⁹ =1-0.3190=0.681

P(at least one other student has your birthday) =1-P(none share birthday with you)

=1-P(all other person has 364 choices except 31st october)=1-(364/365)²⁸ =0.073941