I am trying to figure out some odds for a march madness bracket and I got stuck. I have a list of 6 things that could happen and each of them have different odds of happening (ranging from 85%-3%). I want to know what the odds of at least one of these happening are. I know how to find the "at least one" odds when it's a single number, but I didn't know how to do it for multiple different odds. I tried averaging them all out (which=50%) and doing: 1-(50/100)^6 but I know this isn't correct at all. How would I solve this?
More info: The 6 odds are the percent of times a #16 seed beat #1, #15 beat #2, etc. going down to #6 beating #11.
With the odds referring to different games and none of the same teams involved, we can make the simplifying assumption that the events are independent.
In that case, the best way to find the probability of at least one happening is to calculate the complement. If the probability of the $i$th event happening is $p_i$, the probability of none of them happening is $(1-p_1)(1-p_2)\cdots (1-p_n)$; it's $1-p_1$ that the first doesn't happen, $1-p_2$ that the second doesn't happen, and so on. Then, the probability of at least one happening is $1$ minus that: $$P(\text{at least one}) = 1-(1-p_1)(1-p_2)\cdots(1-p_n)$$