4% Chance per second to trigger an effect...and then it gets complicated

DragonKnight said:

So you can better answer my question I will give you an idea of my personal level of understanding numbers and equations. To begin you should know that I'm not a mathematician by any means. Not even close for that matter. However I can understand and catch on quickly as long as the subject matter interests me. My greatest feat is that I legitimately aced a physics exam in my 2nd college year of an Architectural Technology program utilizing a single practice worksheet the night before the exam. I was inspired to do so because a classmate said he was more intelligent than I could ever be and would embarrass me with his exam results. I proposed to him that if the content of the program were more interesting not only would I care about my results but I could study and pass the course easily with a 95% and to support my claim I would ace the next days exam. I scored 100% because it had a rewarding result.

Be aware I have no experience solving complex probability questions but know that I want to understand this and I have done some reading on types of probability etc so I am semi-confident I will understand how it works if demonstrated before me.

Purpose;

Me and my classmates have to come up with a difficult probability question to present to our professor. I shared a probability question taken from Elder Scrolls Online with my friends and it stumped us...... so before we can ask the question we need to know the answer and the how.

Question;

There is an Item in this game that grants a 4% chance when damaging an enemy with a damage over time effect (DoT) to trigger a meteor that falls out of the sky and crashes into the enemy that set it off. DoT abilities tick for damage once per second (i'll call this a tick-second) It's understood that the 4% chance resets with every tick-second.

If I use 5 separate DoT attacks that each grant a 4% chance per tick-second to trigger the meteor which last 30 seconds each and are applied 1 second apart over 5 seconds, what is the is the probability percentage that the item will trigger the meteor over a 1 minute period?

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Ishuda said:

These type of questions are sometimes best answered if the question is re-worded. Instead of asking what is the chance of something happening is a sequence of events, which has many different ways of happening, ask what is the chance of total failure for something to happen, which has only one way to happen. If you don't have total failure (with probability p say), then you must have success. Since the total probability is 1, the probability of success is 1-p.

For example, suppose you wanted to find the chance of a heads in three coin flips of a fair coin. You could figure out the seven ways you could get at least 1 head, i.e. HTT, HTH, HTT, HHH, etc., and add them up or you could compute the chance of getting 3 tails (total failure) as 1/8 and get the answer of getting at least 1 heads is 1-1/8=7/8.

In regard to your problem, I'm a little unclear as to just what is happening. For example, how long does the DoT last. If it is just the one second, the the total probability of success is 4%. However, if it lasts n seconds, then the chance of triggering at least one meteor event during a DoT is 1-0.96ⁿ. To have a total failure for five DoTs would then be a probability of 0.96⁵ⁿ.

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