system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: If a coin is flipped 1,000 times, would the result of it being head all the 1,000 times be the same as if it was split 50/50?

I had a test last week in math, and it got me thinking. It asked the following question;

"If you toss a coin 4 times, what's the most likely scenario; AAAA, BBBB, ABAB, ABBA."

I chose all of them, can anyone explain me why or why not that is correct or wrong?
gpt
That depends on *how* it is split 50/50.

There's only one way to flip heads 1000 times in a row.

However, there are many ways to flip 500 heads and 500 tails: you could flip 500 heads followed by 500 tails, or flip heads and then tails and then heads and then tails and so on, or flip heads and then 500 tails and then 499 heads, and so on.

But the chance of any *specific* order occurring is equally as likely as any other specific order, since the possibilities for each event are equal and the events are independent.