README.md

In lorenzwalthert/coinflip538: What the Package Does (One Line, Title Case)

coinflip538

The goal of coinflip538 is to solve a 538 puzzle, which goes like this:

If you have a fake coin that returns head with probability 0.6 and a fair coin which returns head and tail with probability 0.5, how many times to you need to flip the coins to know with 95% certainty which coin is fake?

This repo illustrates how to solve this question with base R + tidyverse but no additional statistical library and in a functional programming style. To understand the source code, solve the problem “bottom-up”. I.e. look at p_fair() and p_fake() to compute probabilities of fair and fake coins with just one flip first. Then, conditional independence with p_prod_fair_fake(). Next, we put it together with summing the probabilities resulting form all combinations up (p_fake_gt_fair()) and a final function (p_correctly_identify_coins()) potentially allows for guessing in situations when the heads of both coins have the same count.

Note that every function is just a few lines long, has consistent naming of arguments, variable names, simple input and output.

Installation

library(coinflip538)
data <- tibble::tibble(
  N = 1:150,
  p = purrr::map_dbl(.data$N, p_correctly_identify_coins)
)

ggplot2::ggplot(data, ggplot2::aes(x = N, y = p)) + 
  ggplot2::geom_line()

p_correctly_identify_coins(143, allow_guessing = FALSE)
#> [1] 0.9501282
p_correctly_identify_coins(134)
#> [1] 0.950325

lorenzwalthert/coinflip538 documentation built on May 13, 2019, 11:26 a.m.