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Chapter 2: Q.47 (page 51)

If there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?

Short Answer

Expert verified

The required probability is

P(no two people share their month of birth)=12!1212.

Step by step solution

01

Given Information 

If 12people are in the room:

Outcome space of the experiment is Sx1,x2,x3,…x12:xi∈{1,2,3,…12} where the vector describes their months of birth.

02

Explanation

|S|=1212 because each element of the vector can be chosen in 12 ways.

As each outcome from the outcome space is equally likely, the Axioms give:

A⊆S→P(A)=|A||S|

( |X| is the number of elements in the set X )

And the number of sample events in the event that no two people share their month of birth is 12·11·10·…1=12!, the number of different valued vectors in Sof size 12.

P(no two people share their month of birth)=12!1212

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