D20 probability question How does one calculate the possibility of rolling a 20 between multiple people?
My friends claim that between the four of us, if we each roll 1 d20, we have a 20 percent chance of getting a 20, i dont think this is right but i cant prove why.  
I cant figure out how to calculate an event happening at least 1 in 4 times when each event has a 5 percent chance of happening.
 A: There are two possibilities: Either someone gets a $20$, or no one gets a $20$. Since those two possibilities are exhaustive (there's no way neither could happen) and exclusive (there's no way both could happen at the same time), the sum of their probabilities is $1$.
Now it turns out that "no one gets a $20$" is a much simpler event: The only way this could happen is: You didn't get a $20$, your first friend didn't get a $20$, your second friend didn't get a $20$, and your third friend didn't get a $20$ either.
Now since those events are independent (the result of any of the rolls doesn't depend in any way on the results of the others), the probability of all of them happening is just the product of the individual probabilities. But the individual probabilities here are all the same, namely $19/20$, as there are $19$ other numbers.
Putting it all together, the probability that at least one of you gets a $20$ is
$$P(\text{“no $20$”}) = 1 - \left(\frac{19}{20}\right)^4 = 29679/16000 \approx 0.1855$$
Which for most practical purposes is close enough to the claimed $20\,\%$.
