# What is in Birth Day…

In a class of 50, I had this bet.. There will be atleast 2 people in class who share same birth date(date and month only and not year).

To clarify, person A with DOB 1st January 1999 shares birth day with person  X with DOB 1st January 1965. Years can be different but dates and months are same.

What is probability that such an event might or might not occur?

Before arriving solution to above problem, brief basics of probability..

P(Event) = Count of events that meet condition / Total number Events.

• First person:
• As he / she is first person, DOB can be any of 365 days of total 365 days.
• Second person:
• First person has already chosen a DOB, assuming, in class all of them have different DOB, then there are only 364 days remaining. So probability of second person is 364/365
• Third person:
• First and second already shared DOB,
• Probability: 363/365
• Fifty’th person:
• All prior 49 have already taken 49 days and so there are only 365- 49 days = 316 days. Probability = 316/365

As each person DOB is independent,

Combined Probability: 1×364/365…………316/365 = 0.029626

That implies there is 0.029626 = 0.03 or 3% chances that 2 persons do not share same DOB. Conversely 1-0.29626 = .97034 = 97.034% that there will be atleast 2 persons sharing same DOB.

Find surprising.. try it out..

Until next time..

-Guru