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TIFR CSE 2021 | Part A | Question: 4

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What is the probability that at least two out of four people have their birthdays in the same month, assuming their birthdays are uniformly distributed over the twelve months?

  1. $\frac{25}{48}$
  1. $\frac{5}{8}$
  1. $\frac{5}{12}$
  1. $\frac{41}{96}$
  1. $\frac{55}{96}$
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Answer $(D)$

$P(\text{Atleast two have same birthday month}) = 1 – P(\text{No one have birthday in the same month})$
$= 1 – \frac{12}{12}.\frac{11}{12}.\frac{10}{12}.\frac{9}{12}$

$= \frac{41}{96}$
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