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  3. Foundations of Probability in R

Exercise

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.

Instructions

100 XP
  • 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 fair and biased respectively.
  • 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_11 and biased_11 respectively.
  • 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.