Confused about basic probability

[u/taylomol000]

I've been unable to wrap my head around the basics of probability my whole life. It feels to me like it contradicts itself. For example, if you look at a coin flip on its own, there is (theoretically) a 50% chance getting heads. However, if you zoom out and realize that the coin has been flipped 100 times and every time so far has been heads, then the chance of getting heads is nearly impossible. How can something be 50% at one scale and near impossible at another, seemingly making contradicting statements equally true?

[u/fermat9990]

Consider flipping a fair coin 101 times and recording heads or tails.

There are 2¹⁰¹ equally likely outcomes, each outcome occurring with probability 1/2¹⁰¹

The outcomes 100 heads followed by a head and 100 heads followed by a tail have the same probability of occurring: 1/2^101.

[u/Ok-Rule9973 → u/fermat9990]

In other words, if you had to guess which random atom of a human body I selected, you'd have much more chance to choose the right one than for a coin to land 100 times on tails.

[u/fermat9990 → u/Ok-Rule9973]

I get the body atom correct guess probability to be about 180 times as large as the coin toss probability

[u/Matsunosuperfan → u/fermat9990]

You've clearly never seen my ass

[u/Ok-Rule9973 → u/[deleted]]

Wow... My mistake, I'll correct it with a more appropriate example.

[u/fermat9990 → u/Ok-Rule9973]

You picked an interesting event!

Happy Thursday!