Updating with simulation after 16 heads
We see 16 out of 20 flips from a coin that is either fair (50% chance of heads) or biased (75% chance of heads). How likely is it that the coin is fair?
This exercise is part of the course
Foundations of Probability in R
Exercise instructions
- Simulate 50,000 cases of flipping 20 coins from a fair coin (50% chance of heads), as well as from a biased coin (75% chance of heads). Save these variables as
fairandbiasedrespectively. - Find the number of fair coins where exactly 16/20 came up heads, then the number of biased coins where exactly 16/20 came up heads. Save them as
fair_16andbiased_16respectively. - Print the fraction of all coins that came up heads 16 times that were fair coins- this is the posterior probability that a coin with 16/20 is fair.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Simulate 50000 cases of flipping 20 coins from fair and from biased
fair <-
biased <-
# How many fair cases, and how many biased, led to exactly 16 heads?
fair_16 <-
biased_16 <-
# Find the fraction of fair coins that are 16 out of all coins that were 16