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More updating with priors

Suppose we see 16 heads out of 20 flips, which would normally be strong evidence that the coin is biased. However, suppose we had set a prior probability of a 99% chance that the coin is fair (50% chance of heads), and only a 1% chance that the coin is biased (75% chance of heads).

You'll solve this exercise by finding the exact answer with dbinom() and Bayes' theorem. Recall that Bayes' theorem looks like:

$$\Pr(\mbox{fair}|A)=\frac{\Pr(A|\mbox{fair})\Pr(\mbox{fair})}{\Pr(A|\mbox{fair})\Pr(\mbox{fair})+\Pr(A|\mbox{biased})\Pr(\mbox{biased})}$$

यह अभ्यास पाठ्यक्रम का हिस्सा है

Foundations of Probability in R

पाठ्यक्रम देखें

अभ्यास निर्देश

  • Use dbinom() to calculate the probabilities that a fair coin and a biased coin would result in 16 heads out of 20 flips.
  • Use Bayes' theorem to find the posterior probability that the coin is fair, given that there is a 99% prior probability that the coin is fair.

इंटरैक्टिव व्यावहारिक अभ्यास

इस अभ्यास को इस नमूना कोड को पूरा करके आज़माएँ।

# Use dbinom to find the probability of 16/20 from a fair or biased coin
probability_16_fair <-
probability_16_biased <-

# Use Bayes' theorem to find the posterior probability that the coin is fair
कोड संपादित करें और चलाएँ