Updating with priors
We see 14 out of 20 flips are heads, and start with a 80% chance the coin is fair and a 20% chance it is biased to 75%.
You'll solve this case with simulation, by starting with a "bucket" of 10,000 coins, where 8,000 are fair and 2,000 are biased, and flipping each of them 20 times.
This exercise is part of the course
Foundations of Probability in R
Exercise instructions
- Simulate 8,000 trials of flipping a fair coin 20 times and 2,000 trials of flipping a biased coin 20 times. Save them as
fair_flipsandbiased_flips, respectively. - Find the number of cases that resulted in 14 heads from each coin, saving them as
fair_14andbiased_14respectively. - Find the fraction of all coins that resulted in 14 heads that were fair: this is an estimate of the posterior probability that the coin is fair.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Simulate 8000 cases of flipping a fair coin, and 2000 of a biased coin
fair_flips <-
biased_flips <-
# Find the number of cases from each coin that resulted in 14/20
fair_14 <-
biased_14 <-
# Use these to estimate the posterior probability