Question

Assume for simplicity that n people,all born in april ( a month of 30 days), are collected in a room. consider the event of atleast two people in the room being born on the same date of the month , even if in different years,
e.g. 1980 and 1985. what is the smallest n so that the probablity of this event exceeds 0.5?

Answer 1

7 is the smallest n so that the probability of this event exceeds 0.5

Step-by-step explanation:

Assume for simplicity that n people,all born in april ( a month of 30 days), are collected in a room

Let say there are n people

Probability of being born on any day = 1/30

Probability of not being born on same day = 29/30

Day could by any of the 30 days

P(2) = 30 * ⁿC₂(1/30)²(29/30)ⁿ⁻²  > 0.5

=> ⁿC₂ > 15 * (30/29)ⁿ⁻²

=> n(n-1) > 30 *  (30/29)ⁿ⁻²

n = 7

Smallest  n = 7

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