@littmath August 24 Riddle

gistfile1.txt

##You have 10000 coins. 9999 of them are fair; one is rigged so that it always lands on heads. 
##You choose a coin at random and flip it 10 times; it’s heads all ten times. 
## what is likelihood that the coin is rigged?


ht_list <- rep(list(c("H", "T")), 9999)


ht_list[[10000]] <- c("H", "H")


coins <- tibble(
  x=ht_list
  ) |> 
  mutate(
    coin_id=row_number()
    ,coin_indicator=if_else(coin_id==10000,1,0)
  )

flip_coin <- function(){
coins |> 
  rowwise() |> 
  mutate(
    ten_flips=list(sample(x,size=10,replace=TRUE))
    ,ten_flips=list(str_flatten(ten_flips))
  ) |> 
  unnest(ten_flips) |> 
  filter(
    ten_flips=="HHHHHHHHHH"
  ) |> 
  summarise(
    mean=mean(coin_indicator)
  )
}



results_tbl <- tibble(results=replicate(1000,expr = flip_coin()))

mean_vec <- results_tbl |> unnest(results) |> pull(results) |> mean()


results_tbl |> unnest(results) |> 
  ggplot(aes(x=results))+
  geom_histogram()+
  geom_vline(xintercept = mean_vec,col="midnightblue",size=1)+
  scale_x_continuous(labels = scales::label_percent())+
  theme_classic()