How is it that when you flip a coin 10 times, the likely hood that it’ll land on heads 10 times in a row is extremely small but the likely hood that it’ll land on heads is 50/50 if it already landed on heads 9 times? I get that it’s a closed system and its roughly 50/50 for every coin flip but my brain is just telling me that it should be a higher chance that it would land on tails instead of heads. How does this work?
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I struggled with this for a while too until some one explained it this way:
Image there are two different coin challenges.
* Challenge 1 is to get a single “heads” flip.
* Challenge 2 is to get ***ten*** “heads” flips in a row.
It’s easy to see why for the first challenge your chance at success is 50/50. You have exactly one opportunity to succeed and one opportunity to fail.
Now look at the second challenge. Ten “heads” in a row. Again you have only one opportunity to succeed (getting a heads for every flip), but now you have 10 opportunities to fail. You could get 7 heads in a row, but if you get tails on the 8th flip, then the whole thing fails.
When you think about getting heads 10 times in a row, it’s the second challenge. But when you think about getting heads just one time (even if you’ve gotten heads the last 9 times) it’s still just the first challenge.
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