Awesome q2a theme
0 votes
11 views

there are 27 students in a class.what is the prob that atleast 3 of them have their birthday in the same month?

 

the solution suggested for the question the booklet says avg birthday prob = 27/12 =2.something

so, according to pigeonhole principle, the required probability is 1.

can someone please explain me this.

ago in Probability by (20 points) | 11 views

1 Answer

0 votes

This is a classic pigeonhole principle application.

There are 12 months in a year. So assume 12 rooms, 1 room for each month. You want to put 27 students into these rooms, uniformly. How will you do that ?

  • 1st round, 1 student into each room. Now each room contains 1 student, 15 students remain.
  • 2nd round, 1 student again into each room. Now each room contains 2 students, 3 students remain.
  • 3rd round, you can send the 3 remaining students into any of the rooms. After this, It is guaranteed that some room will have 3 students (if not more).

Hence you can conclude that there will definitely be a room with 3 students. With this analogy, you can conclude that in a group of 27 students, there will surely be at least 3 students whose birthday is in the same month.

And since the event is guaranteed to occur, probability is obviously 1.

ago by (1.2k points)
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
Welcome to GATE CSE Doubts, where you can ask questions and receive answers from other members of the community.
Top Users Jan 2020
  1. shashin

    1163 Points

  2. Vimal Patel

    306 Points

  3. Deepakk Poonia (Dee)

    305 Points

  4. Debapaul

    237 Points

  5. Satbir

    192 Points

  6. SuvasishDutta

    137 Points

  7. Pratyush Priyam Kuan

    118 Points

  8. tp21

    108 Points

  9. pranay562

    95 Points

  10. DukeThunders

    94 Points

Monthly Top User and those within 60% of his/her points will get a share of monthly revenue of GO subject to a minimum payout of Rs. 500. Current monthly budget for Top Users is Rs. 75.
2,983 questions
1,509 answers
8,931 comments
89,814 users