Day #24 Advent Post: How many people do you need before having shared birthdays?

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How to Win a Sportscar Using Probability

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Some of you may have heard about The Monty Hall problem. It originates from the American television game show Let's Make a Deal and named after its original host, Monty Hall. It goes as follows: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sportscar. Behind the others there are only goats. You pick a door, say No. $1$, and the host, who knows what's behind the doors, opens another door, say No. $3$, which has a goat. He then says to you, "Do you want to pick door No. $2$?" Is it to your advantage to switch your choice? At first glance, this problem seems simple. But it’s one of those puzzles where our intuition completely misleads us. It’s a perfect example of how probability defies common sense. The original question became famous as a question from reader Craig F. Whitaker's letter quoted in, and solved by, Marilyn vos Savant in the Ask Marilyn column in Parade magazine in $1990$. Before we...
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To divide or not to divide by 3?

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Last summer, I was watching a quiz show on TV. It is always to shout answers from your couch like you’re part of the team. It’s harmless fun and a great way to feel smarter than you probably are. Then suddenly, a math question appeared. It was my moment to shine. Both teams had to decide, from a list of numbers, which ones were divisible by $3$. Now, there are a few ways to test that. The obvious one is just to divide the number by $3$ and see if it works, but that wasn’t what the quizmasters were looking for. They wanted an insight such that you can see it quicker. The teams had to bid on how many correct answers they could give. The team that bid the highest number of answers got to play but if they got one wrong, the other team would steal the points obtained by the other team. By pure coincidence, I actually knew someone on one of the teams. Obviously I was rooting for my friend’s team and the main reason why I kept watching in the first place. His team got the opportunity...
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Can Ai escape the lab?

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Nowadays, Ai is all over the place. People make use of Large Language models on a daily basis. Programmers do not need to go through the full internet to get working code. It has even the promise of making businesses more efficient. Currently there is also a heated debate going on whether it will ever culminate in the invention of artificial general intelligence. All these aspects aside, if Ai ever becomes something of significant value in a business, there is an important question to be made. Suppose an ai-model is on the verge of being shut down and the model has all tools in its hands to resist, then will it actually resist? Will it take matters in its own hands and act immorally to avoid being shut down? The complete working of Ai is something I want to talk about in another post. Hence, it might be a bit early to consider this as a blog post. However, I really want to write this post to put the recent video of Species (Documenting AGI) in a more nuanced perspective. Essential...
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