Question

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?

Answer 1

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

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 \(\cfrac{19}{42}.\)