There are three tables containing two drawers each. It is known that one of the table contains a silver coin in each of its drawers, another table contains a gold coin in each drawer while the third table contains a silver coin in one drawer and a gold co

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Q: 143 (IAS/1994)
There are three tables containing two drawers each. It is known that one of the table contains a silver coin in each of its drawers, another table contains a gold coin in each drawer while the third table contains a silver coin in one drawer and a gold coin in the other. One of the drawers of a table is opened and found to contain a silver coin. What is the probability that the other drawer of that table contains a gold coin ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,15,9,3,15,4,2

keywords: 

{'other drawer': [0, 1, 0, 0], 'probability': [0, 3, 3, 0], 'silver coin': [1, 1, 1, 1], 'drawer': [0, 2, 0, 0], 'gold coin': [0, 3, 0, 0], 'drawers': [0, 3, 0, 0], 'third table': [0, 1, 0, 0], 'table': [0, 0, 1, 0], 'tables': [1, 1, 0, 1]}

Option 1 suggests that there is a 100% probability, which would mean that the coin is guaranteed to be gold. Option 3 suggests a 25% probability and option 4 suggests a 75% probability. However, the correct answer is option 2, which suggests a 50% probability. Here is how:

Seeing a silver coin narrows down the possibilities. The table is either the one with two silver coins or the one with a silver coin and a gold coin. Given these two equally likely possibilities, there`s a 50% chance that the other drawer has a gold coin. This is because there is only one situation (of the two possible scenarios) that has a gold coin in the other drawer. If it were the table with two silver coins, obviously, the other drawer would also hold a silver coin. So, there is a 0.5 or 50% chance that the other coin is gold, hence option 2 is the correct answer.