Specifically I’m asking about this situation that came up during a D&D game:
Say I’m rolling a 20 sided die, and I do not want to roll a 1. I know that the odds of rolling a 1 are 1/20.
I know that the chances of rolling a 1 twice in a row is (1/20 * 1/20), which is far a lower occurrence.
Say then, before I rolled my “real” roll, I rolled the die again and again until I landed on a 1, then proceeded to roll my “real” roll, would I have reduced the odds of rolling a 1 to (1/20 * 1/20), given that I’ve just rolled a 1 prior?
This is the logic I’m having trouble reasoning about and I’d appreciate it if anyone could clarify what is or is not accurate about the assumptions being made in this scenario.
In: Mathematics
*”To be safer, always bring a bomb with you when you fly. What are the odds of two bombs on the same plane?”*
Your thinking has the same problem as this faux advice. Your decision to bring a bomb has no influence at all on what other people will do. Your other rolls have no influence on what will happen in that particular roll.
The conditional probability of rolling a 1 given that you just rolled a 1 is the same as the probability of rolling a 1 given that you just ate a glazed donut. It’s still 1/20. The die has no memory of the past.
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