From a random sample of twenty persons, how likely is it for atleast two persons to share a birthday?

Since this tiny statistic bopped at me twice already, i thought i'll just bopped it at you guys too. Answers can range from one percent to one in a million, in general, the consensus is usually unlikely.

Quite on the contrary, the answer to the question is closer to 50%. See article here.

Excerpt :
"The explanation for this is that there is a large number of pairs of students upon whom the coincidence may fall. For 23 students, there are 231 ways (22×21÷2) of picking two students from the class, which means 231 potential coincidences that may occur. We expect pairs to have the same birthday once in every 365 times, so with 231 pairs it is unsurprising when one of them strikes lucky."

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For those planning to spend more than $100 at the upcoming casinos integrated resorts (entrance fee is $100), do continue reading the link about Gambler's Fallacy. Basically, if you've lost many times already, it doesn't make your next chance at winning higher.

If you flip a coin 999 times and each time you flipped heads. The chance of flipping heads the 1000th time is not 1 / (2 ^ 1000). It's still 1/2. Why? Coz the coin has no memory of its previous flips. The probability of arriving at 1000 heads is indeed 1 / (2 ^ 1000) but the likelihood of getting a head for that flip is still 1/2! Perhaps rewriting the probability of a thousand heads would help. The probability is : (1 / (2 ^ 999)) x (1/2)

It is important to note that normally you're not betting on 1000 flips being head but you're betting on every flip along the way. If you're gambling, do not commit Gambler's Fallacy. Stop if you keep losing.

Disclaimer : I might get the mathmatics wrong, if i do, let me know.

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