Question

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

• A. $\frac{4}{7}$
• B. $\frac{3}{4}$
• C. $\frac{3}{7}$
• D. $\frac{37}{56}$

Answer 1

The correct option is D $\frac{37}{56}$

There are equal chances of choosing either purse, i.e.,
$P$(1st purse)$=P$(2nd purse)$=\frac{1}{2}$
The probability that the first purse is chosen and a copper coin is drawn $=\frac{1}{2}\times \frac{4}{7}$
The probability that the first purse is chosen and a copper coin is drawn $=\frac{1}{2}\times \frac{6}{8}$
Since, the events are mutually exclusive, so by using addition theorem, we have
Required probability$=\frac{1}{2}.\frac{4}{7}+\frac{1}{2}.\frac{6}{8}=\frac{37}{56}.$