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July 25th, 2018, 06:04 AM   #1
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Question 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.
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July 25th, 2018, 06:36 AM   #2
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Does the value of r have to be a whole number?
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July 25th, 2018, 08:30 AM   #3
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Yes, the number r is always an integer.
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July 25th, 2018, 08:41 AM   #4
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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

$P[\text{wood, stone, metal}] = \dfrac{\text{number of values of }r \text{,
such that }1 \leq r \leq 75}{\text{total possible values of }r} = \dfrac{75}{100} = \dfrac 3 4$
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July 25th, 2018, 08:49 AM   #5
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Yeah, that probably is the better assumption. Thanks for helping out .
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