So I have a math probablity question.
Lets say there is a pile of money that I can win. I get 15 random numbers assigned to me (i get no say in the matter) and then a number out of 100 is drawn at random. If I hit on that 15% chance I win the money.
Now lets say I get three shots. Get 15 random numbers, number gets drawn out of 100 if I win I win game stops, If i lose we do it again. Get 15 random numbers, number gets drawn out of 100 if I win I win if I lose we do it again. Get 15 random numbers, number gets drawn out of 100 if I win I win if I lose I lose.
So basically I have a 15% chance of winning three times.. what is my overall chances of winning the money?
In: 2
Start from this:
You have a formula for “what is the chance of a thing happening *every* time”, and that’s to multiply the chances of each trial together.
A chance of a coin flip being heads both times in two flips is 1/4, because each flip had a 1/2 chance, and 1/4 is 1/2 of 1/2.
A chance of a coin flip being heads 3 times in 3 flips is 1/8, because that’s 1/2 of 1/2 of 1/2.
So if you have this rule, then you can invert the odds of it to figure out your chances of FAILING to have a thing happen every time.
If your odds of getting 3 heads in 3 flips is 1/8, from the above, then your odds of getting anything OTHER than 3 heads in those 3 flips is the remaining 7/8. (which is 1 – 1/8).
So you do that here with your example. If success means you just have to hit 15% once in 3 tries, that’s the inverse of saying “to fail you have to hit 85% every time for 3 tries.”
And the odds of hitting 85% three times in a row is 85% of 85% of 85%.
Which is 61.4125%. That’s your chance of NOT hitting 15% 3 times in a row.
So the inverse of that is your chance of hitting 15% at least once out of 3 tries: 100% – 61.4124% = 38.5875%.
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