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July 25th, 2018, 06:04 AM  #1 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0  Calculate probability of interval with a random variable?
Hi! I have studied algebra and calculus mostly (Calculus 1), not so much probability. So my problem is that I have a random variable called r that can generate any number from 1 to 100 (1 and 100 are included, interval [1, 100]). I set up a condition that if r >= 1 and r <= 75 then generate a wood, stone or metal block, but if r >= 75 and r <= 100 then generate a emerald, ruby or diamond block. So in the first condition (interval) there is a greater chance of generating some of these blocks than there is in the second condition (interval), I assume, but how can I calculate the probability of the interval? Or calculate the interval to get a certain probability? I already know that I want a 75% chance for the easier blocks to generate and 25% for harder blocks to generate. Last edited by DecoratorFawn82; July 25th, 2018 at 06:08 AM. 
July 25th, 2018, 06:36 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
Does the value of r have to be a whole number?

July 25th, 2018, 08:30 AM  #3 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 
Yes, the number r is always an integer.

July 25th, 2018, 08:41 AM  #4 
Senior Member Joined: Sep 2015 From: USA Posts: 2,122 Thanks: 1102 
We have to assume that $r$ is a uniform random variable in the absence of any other information regarding it's distribution. We also have to correct your conditions a bit assuming we never generate two blocks. I'm going to assume you generate the harder blocks if $75 < r \leq 100$, i.e. $r=75$ generates a block in the first group, not the second. Given this assumption we can compute the probability of wood, stone, or metal as $P[\text{wood, stone, metal}] = \dfrac{\text{number of values of }r \text{, such that }1 \leq r \leq 75}{\text{total possible values of }r} = \dfrac{75}{100} = \dfrac 3 4$ 
July 25th, 2018, 08:49 AM  #5 
Member Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 
Yeah, that probably is the better assumption. Thanks for helping out .


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calculate, interval, probability, random, variable 
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