Updating with simulation
We see 11 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? Answer this by simulating 50,000 fair coins and 50,000 biased coins.
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 11/20 came up heads, then the number of biased coins where exactly 11/20 came up heads. Save them as
fair_11andbiased_11respectively. - Find the fraction of all coins that came up heads 11 times that were fair coins- this is the posterior probability that a coin with 11/20 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 11 heads?
fair_11 <-
biased_11 <-
# Find the fraction of fair coins that are 11 out of all coins that were 11