A table has three drawers. It is known that one of the drawers contains two silver coins, another contains two gold coins and the third one contains a silver coin and a gold coin. One of the drawers is opened at random and a coin is drawn. It is found to

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Q: 142 (IAS/1995)
A table has three drawers. It is known that one of the drawers contains two silver coins, another contains two gold coins and the third one contains a silver coin and a gold coin. One of the drawers is opened at random and a coin is drawn. It is found to be a silver coin. What is the probability that the other coin in the drawer is a gold coin ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,13,6,1,5,13,0

keywords: 

{'silver coin': [1, 1, 1, 1], 'gold coin': [0, 3, 0, 0], 'silver coins': [0, 4, 0, 0], 'probability': [0, 3, 3, 0], 'gold coins': [2, 0, 1, 0], 'drawer': [0, 2, 0, 0], 'drawers': [0, 3, 0, 0], 'coin': [0, 3, 6, 4], 'other coin': [0, 1, 0, 0], 'table': [0, 0, 1, 0]}

We have three drawers, so we randomly open one and draw out a silver coin, which means we have two scenarios:

Option 1: The drawer contains two silver coins (SS)

Option 2: The drawer contains one silver coin and one gold coin (SG)

Option-1(0.25) and Option-4(0.60) can be ruled out as the probability in such cases can never be beyond one or less than zero.

Looking at Option-2(1.00), this would mean certainty. However, we have two possible scenarios, not just one, so it can`t be 100% certain that the other coin is gold.

Option-3(0.50) is the correct answer because out of your two possible scenarios for having a silver coin (SS and SG), in one of them (SG), the other coin will be gold. So one out of two scenarios is desired, which is a probability of 0.5. Hence, the probability that the other coin in the drawer is a gold coin is 0.5 or Option-3.