Probability Calculator

This plugin provides a tool for calculating various probabilities for statistical mechanics in OSRS. (Currently only calculates drop rates.)

Drop Rates

How to Use

1. Enter the probability of 1 successful trial (drop rate).

2. Enter the amount of total trials (kill count).

3. Enter the amount of successful trials (number of actual drops received).

4. Calculate and cry.

#### Configuration

You may configure how many decimal places the output will round up to in the configuration panel of the plugin. The default is set to 2 decimal places.

The Math

Drop rates are calculated as binomial distributions:

<code>P(x) = _nC_x p^x (1-p)^n-x</code>

<p>

where:<br>

<code>n</code> is the number of trials<br>

<code>x</code> is the number of successful trials<br>

<code>p</code> is the probability of one success<br>

<code>_nC_x</code> is "n choose x" which equals <code>n!/x!(n-x)!</code>

</p>

• To calculate the probability of getting exactly x successes would be to calculate

<code>P(X=x)</code>.

• To calculate the probability of getting at least x successes would be to calculate

<code>P(X>=x)</code>. This equates to <code>P(X=x) + P(X=x+1) + P(X=x+2) + ... + P(X=n)</code>.

• To calculate the probability of getting zero successes would be to calculate

<code>P(X=0)</code>.

If we wish to calculate the probability of getting at least 1 drop, then we solve for <code>P(X>=1)</code>. Instead of solving for the sum of every probability at <code>x=1</code> and up, we can instead solve for its complement and subtract it from 1. Therefore, <code>P(X>=1) = 1 - P(X=0)</code>.

Solving for <code>P(X=0)</code> is quite simple, since <code>_nC_x=0</code> and <code>p^x=0</code> will always be equal to 1. Therefore, the binomial equation simplifies to <code>P(X=0) = (1-p)ⁿ</code>. This is the same equation you would use to determine the chances of getting no drops. Simply subtracting this from 1 as previously mentioned will yield the probability of getting at least 1 drop in <code>n</code> kills.