Question

Suppose we have four chests each having two drawers. Chests 1 and 2 have a gold coin in one drawer and a silver coin in the other drawer. Chest 3 has two gold coins and chest 4 have two silver coins in each drawer. A chest is selected at random and a drawer opened. It is found to contain a gold coin. Find the probability that the other drawer has: (a) a silver coin, (b) a gold coin.

Answer 1

The probability that the other drawer has (a) a silver coin is $\frac{2}{3}$ and (b) a gold coin is $\frac{1}{3}$.

• Given,
• There are 4 chests with 2 drawers each.
• Chest 1 and chest 2 contain one gold and one silver coin in their drawers.
• Chest 3 contain both gold coins in each of the drawer.
• Chest 4 contain both silver coins in each of the drawer.
• Since a chest is selected at random and found a gold coin.
• The probability that the other drawer has
• (a) a silver coin
• Since chests 3 and 4 contains both gold and silver coins respectively, these two get cancelled as they don't contain single gold and silver coins. We need to consider only 2 chests out of 4 chests, as chests 1 and 2 contain both one gold and one silver coins.
• Hence the probability becomes,
• $P(A)=\dfrac{2}{3}$
• (b) a gold coin
• Since one gold coin is already drawn, hence to find the probability that other coin is also a gold coin, we need to consider chest 3, as out of 4 chests, only chest 3 contains both the gold coins in it's drawer.
• Hence the probability becomes,
• $P(B)=\dfrac{1}{3}$

Answer 2

probability of Silver coin = 2/3  & probability of Gold coin = 1/3

Step-by-step explanation:

Chest 1 :   Gold  Silver

Chest 2 :  Gold Silver

Chest 3 :  Gold Gold

Chest 4 :  Silver Silver

A chest is selected at random and a drawer opened. It is found to contain a gold coin

=> Drawer Selected in one of the First Three drawers

as drawer 4 does not have Gold coin

if Selected Drawer is Chest 1 & Chest 2

then other drawer will have Silver coin

if Selected Drawer is Chest 3 then other drawer will have gold coin

So

probability of Silver coin = 2/3

& probability of Gold coin = 1/3

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