Unable to approach this question. Kindly help.
Birthday Paradox
In order to solve this question we have to think in terms of probability.
So, P(same) = 1 - P(different) this means that probability that two people have their birthday on same day is 1 minus the probability that none of them have birthday on same day. Now we can easily calculate the value for P(different) it’ll be
1 x (1 – 1/365) x (1 – 2/365) x (1 – 3/365) x …. x (1 – (n-1)/365
How to get this expression, The first person can have any birthday among 365, The second person should have a birthday which is not same as first person so 364 days are available to choose from and so on.
Now we will approximate value of P(different) and plug it into P(same) = 1 - P(different) to get the value for P(same), which will give us a relationship between p and n which we’ll use to solve this question.
Relationship is, if p is the given probability then
Probability (a) = log(1/1-p) and minimum number of people = sqrt (2.365.a).
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