Answer :

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 E_{1} be the event that the first purse is selected and E_{2} 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 E_{3} denote the event that a silver coin is pulled.

Hence, we have

We also have

Using the theorem of total probability, we get

P(E_{3}) = P(E_{1})P(E_{3}|E_{1}) + P(E_{2})P(E_{3}|E_{2})

Thus, the probability of pulling a silver coin is.

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