i HAVE ATTACHED THE PROBLEM STATEMENT IMAGE .CAN ANYONE SOLVE THIS PROBLEM WITH LOGIC AND NOT USING BAYES THEOREM.

E1 represents the selection of Box I

E2 represents Selection of Box II

And E3 represents the Selection of Box III

Let A denotes the event such that the coin drawn is of gold.

∵ there are 3 boxes-

∴ P(E1) = P(E2) = P(E3) = 1/3

Since, all boxes contains two coins.

And box I have both the coins gold.

Box II has only silver coins, and box III has one gold and one silver coin.

∴ P(A|E1) = P(drawing gold coin from box I) = 2/2 = 1

Similarly, P(A|E2) = 0

And P(A|E3) = 1/2

We need to find the probability of the event such that another coin in the box is also gold and this is only possible if the coin is drawn from the box I

i.e. we need to find P(E1|A).

From Baye’s theorem–

⇒ P(E1|A) =

∴ The probability that the other coin in the box is also of gold = 2/3