It’s time to do one Bayes’ theorem exercise. The problem is known as the Bertrand box paradox and may remind us of the boy or girl paradox.
Imagine there are three boxes. One contains two gold coins, the second two silver, and the third has one gold and one silver. Now you randomly pick a box and take out one coin. If that turned out to be silver, what is the probability that the other coin in that box is also silver?
Intuition suggests that the other coin could either be silver or gold. And therefore, it would be tempting to answer 50%. But that is not true. Let’s apply Bayes’s theorem straightaway. The required probability is mathematically equivalent to the chance of getting two silver (SS), given that one coin is already silver (S) or P(SS|S).
G represents gold and S, silver.
