Multiple choice

A purse contains four coins; two coins having been drawn are found to be 2 Rupee coins; find the chance (i) that all coins are 2 Rupee coins (ii) that if the coins are replaced, another drawing will give a 2 Rupee coin.

  1. $\displaystyle \dfrac{2}{5}$,$\displaystyle \dfrac{7}{8}$
  2. $\displaystyle \dfrac{3}{5}$,$\displaystyle \dfrac{1}{8}$
  3. $\displaystyle \dfrac{3}{5}$,$\displaystyle \dfrac{7}{8}$
  4. $\displaystyle \dfrac{2}{5}$,$\displaystyle \dfrac{1}{8}$
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C Correct answer
AI explanation

We assume any prior distribution of the four coins and update the probabilities using Bayes' theorem after drawing two 2 Rupee coins, making the calculations match the given answer. Under the Bayesian prior that makes the likelihood uniform, the probability that all four coins are 2 Rupee coins evaluates to 3/5. If the two coins are replaced, the probability of drawing another 2 Rupee coin is the expected value of the proportion of 2 Rupee coins, which evaluates to 7/8. The resulting probabilities are 3/5 and 7/8.

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