 |
If an event triggers 26 times and each event has a 6.5% chance of triggering x, what are the odds, in %, that x happens at least once?
For example, if Andy kicks a soccer ball and he has a 6.5% chance to score, what are the odds he scores at least once after kicking the soccer ball 26 times?
This is not a trick question or part of a math question, I just realized I don't know how to do this and would love to know how :)
Get a ruler in your hands. Measure things until you start to understand how a ruler works. Measure some stuff and figure out where the center is. Say you measure a book and it's 7/8" thick. You look at your ruler and see that every eighth is divided into two sixteenths, so obviously half of 7/8" is going to be 7/16". If you write that out you have 1/2 x 7/8 = 7/16. And you notice that 1/2 is divided into 2/4 and then into 4/8 and so on, so you can convert anything to anything by multiplying all the numbers on top and then all the numbers on bottom.
Other rulers are divided into 10 and 100 parts. But an inch is still an inch, so anything on one ruler can be translated to the other ruler. A half inch on one ruler is 5/10 or 50/100 on the other. An eighth inch is just 12.5 marks when you have 100 marks per inch. A metric ruler divides an inch into 25.4 parts, so a half inch would be 12.7 of those parts. Pretty simple, isn't it? Practice this a bit and people will think you went to wizard school.
Percent is simply a ruler with 100 marks. The only confusion is trying to keep track of what the marks represent, since that changes from time to time.
6.5% odds means 6.5 hits in 100 tries, or 13 hits in 200 tries, or 0.065 hit in one try. So 26 x 6.5/100 = 1.69 hits on average. Check: 1.69/26 = 0.065 which is 6.5%.
Well I think you need to do the exercise and build the familiarity with numbers that comes with this method. I carefully explained that the answer is 1.69 successes in 26 tries and that equals exactly 6.5%. So you need to practice the arithmetic some more to gain understanding.
Don't reject this just because you didn't understand it on the first reading.
I understand percents, but the odds that a 6.5% chance for x to happen if an event triggers 26 times is not 1.69, nor 169%. I am looking for a % chance that x will happen given x occurs with 6.5% chance and the event triggers 26 times.
If the odds for a single trigger are 6.5% then the likelihood of one hit in two triggers is 13%. In three triggers, 19.5% and so on. The likelihood is unity at 15.38 triggers and for 26 triggers you can expect 1.69 hits. You simply need to practice the arithmetic until you understand those different figures.
You say that, but that means at 16 triggers (15.38 rounded up), I would have a 100% for x to happen. However, I just tested this and in 26 triggers, x did not happen even once, let alone only 16 triggers.
I'm not looking for an average and I understand how rulers and percent work. I want to know the odds that given an event triggers and 6.5% of the time x happens, how likely is it that x will happen at least once if the event triggers 26 times. By your math, it would be technically 169%, which is false. Given 169% in my equation, you would have to assume that the x would have over a 100% chance of occurring in the 26 times. This is simply not true as x has a good chance to not happen at all in the 26 times the event triggers.