Given three identical boxes I, II and III, each containing two coins. In box L 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?

Explanation

To solve the problem step by step, we will use Bayes' theorem. Let's denote the events as follows:

- Let \( B_1 \): the event that box I is chosen (contains 2 gold coins).
- Let \( B_2 \): the event that box II is chosen (contains 2 silver coins).
- Let \( B_3 \): the event that box III is chosen (contains 1 gold and 1 silver coin).
- Let \( E \): the event that a gold coin is drawn.

We want to find \( P(B_1 | E) \), the probability that box I was chosen given that a gold coin was drawn.
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