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
This is actually relatively simple to calculate.
To find the probability of winning at least once in three attempts, find the probability of not winning in three attempts, and subtract it from 1.
The probably of not winning a game is 85%, or 0.85.
The probability of not winning three times is 0.85*0.85 *0.85. 0.85^(3)
And then the probability of winning at least once is 1 – 0.85^(3)
Which gives 0.3859. About 39%.
And you can plug in any number of attempts into the same formula to figure it out.
If you draw a number 5 times, it’s 1 – 0.85^(5) = 0.56.
So you only need to draw a number 5 times before you’re more likely to win than lose. That’s nice.
This is all assuming that the different draws are independent, i.e. any number can be picked more than once.
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