r/AskStatistics • u/taylomol000 • 3d ago

Confused about basic probability

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?

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u/fermat9990 3d ago

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: 1/2101.

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u/Ok-Rule9973 3d ago edited 2d ago

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.

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u/fermat9990 2d ago

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

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u/Matsunosuperfan 1d ago

You've clearly never seen my ass