![coin flip simulator coin flip simulator](https://i.stack.imgur.com/dxywt.png)
We can then visualize the probability that there are no streaks as a function of the number of flips in the sequence. This takes about 5 seconds on my machine. 5 )) %>% mutate ( no_three = map_lgl ( flips, no_three_heads )) %>% group_by ( sequence_length ) %>% summarize ( chance_no_three = mean ( no_three )) sim # A tibble: 25 x 2 # We'll say 1 is heads, 0 is tails flips % mutate ( flips = map ( sequence_length, rbinom, 1.
![coin flip simulator coin flip simulator](https://i.ytimg.com/vi/YSn6lYOHBIs/maxresdefault.jpg)
Let’s start with values \(n=20 k=3\): what’s the probability that a sequence of 20 flips contains no streaks of length 3? You can flip a sequence of coins with rbinom(). (In the process, we also see how we’d calculate a Fibonacci sequence in one line!) Simulating a single sequence
#Coin flip simulator series#
To continue my series of simulating probability puzzles in the tidyverse, I’d like to show how we’d approach simulating Feller’s coin-tossing problem, and comparing it to the exact values. H/t #rstats /V0zgOmCy7t- David Robinson June 17, 2018 This reminds me a bit of one of my earlier tidyverse simulations:Ī #tidyverse simulation to demonstrate that if you wait for two heads in a row, it takes 6 flips on average, while you wait for a heads then a tails, it takes 4 flips on average Note that while the number of heads in a sequence is governed by the binomial distribution, the presence of consecutive heads is a bit more complicated, because the presence of a streak at various points in the sequence isn’t independent.
![coin flip simulator coin flip simulator](https://i.ytimg.com/vi/P_724IzjrL4/maxresdefault.jpg)
If you flip a coin \(n\) times, what is the probability there are no streaks of \(k\) heads in a row? Mathematician William Feller posed the following problem: (I recommend the book if you like the topic too!) I recently learned about Feller’s coin-tossing puzzle, from the book Mathematical Constants by Steven Finch. I have an interest in probability puzzles and riddles, and especially in simulating them in R. The “largest stock profit or loss” puzzle.The “knight on an infinite chessboard” puzzle.