# A purse contains 2 silver and 4 copper coins. A second purse contains 4 silver and 3 copper coins. If a coin is pulled at random from one of the two purses, what is the probability that it is a silver coin?

Given:

First purse contains 2 silver and 4 copper coins.

Second purse contains 4 silver and 3 copper coins.

A coin is pulled a random from one of the two purses.

There are two mutually exclusive ways to pull a silver coin from one of the two purses –

a. The first purse is selected, and then, a silver coin is pulled from the first purse

b. The second purse is selected, and then, a silver coin is pulled from the second purse

Let E1 be the event that the first purse is selected and E2 be the event that the second purse is selected.

Since there are only two purses and each purse has an equal probability of being selected, we have

Let E3 denote the event that a silver coin is pulled.

Hence, we have

We also have

Using the theorem of total probability, we get

P(E3) = P(E1)P(E3|E1) + P(E2)P(E3|E2)

Thus, the probability of pulling a silver coin is.

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