A purse contains 4 copper and 3 silver coins, and a second purse contains 6 copper and 2 silver coins. A coin is taken out from any purse, the probability that it is a copper coin is 

Let E 1 = Event of choosing purse I 

E2 = Event of choosing purse II

 A = Event that the coin drawn is of copper. 

$\therefore P\left(E_1\right)=\frac{1}{2}=P\left(E_2\right)\therefore P\left(A/E_1\right)=\frac{4}{7},P\left(A/E_2\right)=\frac{3}{4}$

By theorem of total probability, 

$P\left(A\right)=P\left(E_1\right)P\left(A/E_1\right)+P\left(E_2\right)P\left(A/E_2\right)=\frac{1}{2}\times \frac{4}{7}+\frac{1}{2}\times \frac{3}{4}=\frac{37}{56}$