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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

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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.

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