Like. I know they are different and that one is less likely. But could someone explain this in a way that I can explain it to my partner? I know it is true but cannot remember anything about why and how to explain my point.
In: 6
Assuming the 7% chances are independent events like a weighted coin flip, the chances are waaaayyyy smaller than 7% if you flip it 10 times and certainly minuscule compared to 70% lol! You see the problem with multiple independent events is that they multiply by a power of the chance so that if you had a 7% chance of getting heads, the chance of you getting heads 10 times is 0.07^10 which is 2.82*10^-12 or 2.82*10^-10 %. That is astronomically small. Think about a normal coin flip with 50% chance of getting heads. Well the first time you flip it’s a 50% chance of getting heads. There are 4 combinations however of coin flips in 2 flips (HH, HT, TH, TT) so the chance of getting heads twice is 25%. In three flips there are 8 combinations of events so it’s 12.5% for all 3 to be heads. You get the gist.
So clearly a 70% chance is extraordinarily more favorable than 10 7% chances unless you only require one instance of the 10 events to be that 7% probability. In that case the chance that it never happens is 0.93^10 or ~48.4% because there’s a 93% chance of said event never occurring. So the chance of your 7% chance event occurring at least once in 10 instances of the same independent event are 100-48.4 or 51.6%. Still less than 70%
The math gets a bit more complicated if the events are dependent on previous outcomes or other factors.
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