Question

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

• A. $\frac{4}{7}$
• B. $\frac{3}{4}$
• C. $\frac{37}{56}$
• D. None of these

Answer 1

The correct option is C

$\frac{37}{56}$

Explanation for the correct option:

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

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

$\begin{array}{rcl}p\left(s_1\right)& =& \frac{1}{2}·\frac{4}{7}\\ & =& \frac{2}{7}\end{array}$

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

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

$\begin{array}{rcl}p\left(s_2\right)& =& \frac{1}{2}·\frac{6}{8}\\ & =& \frac{3}{8}\end{array}$

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.

$\begin{array}{rcl}p\left(s\right)& =& p\left(s_1\right)+p\left(s_2\right)\\ & =& \frac{2}{7}+\frac{3}{8}\\ & =& \frac{37}{56}\end{array}$

Hence, option (C) is the correct answer.