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Single-event probability

Can you help me understand how to solve this problem? (I need the process and math behind it, not just the answer).
Suppose I have a 10-sided die. It's clear enough that the odds of rolling a 1 are 10% for any single roll. What, then, is the likelihood that I will roll a 1 given 10 rolls? Given 5 or 20 rolls?
I'd need to solve this for any single-event probability, too -- not just for a 10-sided die.

Solution Preview

Solution. We first consider a 10-sided die. Then we can generalize this idea to any m-sided die. Obviously, if we roll a 10-sided die, we get 1 with probability p=10%.
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<br>(1) If we roll this die 10 times, then denote the number that we get 1 by X. We know that X is a random variable which ...

Solution Summary

Can you help me understand how to solve this problem? (I need the process and math behind it, not just the answer).
Suppose I have a 10-sided die. It's clear enough that the odds of rolling a 1 are 10% for any single roll. What, then, is the likelihood that I will roll a 1 given 10 rolls? Given 5 or 20 rolls?
I'd need to solve this for any single-event probability, too -- not just for a 10-sided die.

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