Each of 2 cabinets identical in appearance has 2 drawers. cabinet a contains a silver coin in each drawer, and cabinet b contains a silver coin in one of its drawers and a gold coin in the other. a cabinet is randomly selected, one of its drawers is opened, and a silver coin is found. what is the probability that there is a silver coin in the other drawer?

The probability that there is a silver coin in the other drawer is

Step-by-step explanation:

Given : Each of 2 cabinets identical in appearance has 2 drawers. Cabinet A contains a silver coin in each drawer, and cabinet B contains a silver coin in one of its drawers and a gold coin in the other. A cabinet is randomly selected, one of its drawers is opened, and a silver coin is found.

To find : What is the probability that there is a silver coin in the other drawer?

Solution :

Let A be the event that cabinet A is chosen.

Let B be the event that cabinet B is chosen

Let E be the event that silver coin is chosen.

Each of 2 cabinets identical in appearance has 2 drawers.

So,

Cabinet A contains a silver coin in each drawer,

i.e.

Cabinet B contains a silver coin in one of its drawers and a gold coin in the other,

i.e.

The probability that there is a silver coin in the other drawer is given by,

Applying Bayes theorem,

Therefore, the probability that there is a silver coin in the other drawer is

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