Probabilities in simple random samples

1 Introduction

When it comes to math, one of the things that people are phenomenally bad at – aside from the obvious everything – is probabilities. Specifically, calculating probabilities. People are bad enough at estimating chances, but properly calculating then has its own hurdles.

In this particular case, I'd like to take a look at the probability of a Simple random sample: getting a particular distribution of results from a number of samples, like getting 3 sixes in a certain number of rolls. Specifically, I'll look at the case with replacement. In this case, the sample pool remains the same after each individual sample. The case without replacement (like picking colored marbles from a vase without putting them back) is a bit trickier so I won't cover that now.

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