How many people do you need in a room so that you expect that there is going to be a shared birthday on a Monday of the year (assume 52 Mondays in a year and 365 days in a year) ? By "expect" we mean on expectation, there should be 1 pair of people that have a shared birthday'

Question

Mathematics

Rohan Johnston

1 September, 13:31

How many people do you need in a room so that you expect that there is going to be a shared birthday on a Monday of the year (assume 52 Mondays in a year and 365 days in a year) ? By "expect" we mean on expectation, there should be 1 pair of people that have a shared birthday'

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Aurora Chung · Answer 1

Step-by-step explanation:

Given that the year is having only 365 days (not a leap year)

P (anyday as birthday) = 1/365

Any body will have a chance of having on Monday the birthday

=52/365 (assuming 52 Mondays as given)

Hence we can expect 365/52 = 7.019

i. e. if 7.019 persons are present there will be a definite chance for any other person to share this birthday

Hence atleast 8 people we need in a room so that you expect that there is going to be a shared birthday on a Monday of the year