Question
Given three identical boxes I, II and III, each containing two coins. In box I. both coins are gold coins, in box. II, both are silver coins and in the box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin, if the coin is of gold, what is the probability that the other coin in the box is also of gold?
Solution
Let E1, E2 and E3 be the events that boxes I, II and III are chosen, respectively.
Then
Let A be the event that 'the coin drawn is of gold'
Then
Then
Let A be the event that 'the coin drawn is of gold'
Then
Now. the probability that the other coin in the box is of gold
= the probability that gold coin is drawn from the box I
= P(E1 | A)
By Bayes’ theorem, we know that
