There are three drawers in a table. One contains two gold coins, another two silver coins, and the third, a silver coin and a gold coin. One of the drawers is pulled out and a coin is taken out. It turns out to be a silver coin. What is the probability of

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Submitted by examrobotsa on

Q: 135 (IAS/1997)
There are three drawers in a table. One contains two gold coins, another two silver coins, and the third, a silver coin and a gold coin. One of the drawers is pulled out and a coin is taken out. It turns out to be a silver coin. What is the probability of drawing a gold coin, if one of the other two drawers is pulled out next and one of the coins in it is drawn at random ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,4,2,2,4,0,0

keywords: 

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

The question involves conditional probability.

Option 1 - 37.5%: This is not correct because even if we consider the drawer having one silver and one gold coin, the probability of pulling out a gold coin is 50%, not 37.5%.

Option 2 - 50%: This is correct. One drawer is already out of consideration because it had a silver coin pulled from it already. We have the other two drawers left. One has two gold coins and the other has one silver and one gold coin. So, the total possibilities are 3 where 2 are gold coins. As such, the probability of drawing a gold coin is 2/3 = 0.67 or 66.67%, and the probability for silver is 1/3 or 33.33%. Thus, The probability of drawing a gold coin, if one of the other two drawers is pulled out is 50%.

Option 3 - 62.5%: This is not correct. It seems too high for any possible combination of coins remaining in the drawers.

Option 4 - 75%: This is not correct either as it also exceeds the logical probability of pulling out a gold coin from any of the remaining drawers.