#probability

#probability

The ability to forecast the future is a valuable sign of intelligence and a good test of AI's capabilities. How good is ChatGPT at prediction? An answer to this fascinating question emerged recently when economist David Seif wrapped up an annual forecasting contest he runs for a secret group of economists, hedge fund investors, and tech executives. In its seventh year, the challenge requires contestants to predict roughly 30 events.

If you've ever shuffled a deck of playing cards, you've most likely created a unique deck. That is, you're probably the only person who has ever arranged the cards in precisely that order. Although this claim sounds incredible, it's a great illustration of how quickly large numbers can creep into everyday situationswith occasionally challenging consequences, as the developers of an online poker game painfully discovered in the late 1990s.

Chance of Winning For Powerball, you pick five random numbers out of the digits 1 through 69, plus a Powerball number from 1 to 26. This math is simple: With a single ticket, your chance of winning is one in 292,201,338. If you buy two tickets and run different numbers, your odds are two in 292,201,338not much better!and so on. You may think, Okay, I'm going all out this time. I'm spending $50 to buy 25 tickets. Your chance is now 25 out of 292 million, which is still, sorry to say, infinitesimal.

If the lone glove left behind is red, both octopuses can wear green gloves. If the lone glove left behind is green, both octopuses can wear red gloves.

The chances that no three sticks can form a triangle are connected to the Fibonacci sequence, illustrating a surprising relationship between geometry and nature.