Question

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

• A. $\frac{37}{56}$
• B. $\frac{19}{56}$
• C. $\frac{4}{7}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B

$\frac{19}{56}$

Explanation for the correct option:

Step 1: Find the probability that a silver coin comes when taken from the first purse:

Find the probability by selecting the first purse and then picking a silver coin from it.

$\begin{array}{rcl}p\left(s_1\right)& =& \frac{1}{2}·\frac{3}{7}\\ & =& \frac{3}{14}\end{array}$

Step 2: Find the probability that a silver coin comes when taken from the second purse:

Find the probability by selecting the second purse and then picking a silver coin from it.

$\begin{array}{rcl}p\left(s_2\right)& =& \frac{1}{2}·\frac{2}{8}\\ & =& \frac{1}{8}\end{array}$

Step 3: Find the total probability that a silver coin comes from any purse:

Find the probability by adding up the sum of the probability of each purse.

$\begin{array}{rcl}p\left(s\right)& =& p\left(s_1\right)+p\left(s_2\right)\\ & =& \frac{3}{14}+\frac{1}{8}\\ & =& \frac{19}{56}\end{array}$

Hence, option (B) is the correct answer.