Question

A purse contains $4$ copper coins and $3$ silver coins. A second purse contains $6$ copper coins and $4$ silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?

• A. $\frac{41}{70}$
• B. $\frac{31}{70}$
• C. $\frac{27}{70}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{41}{70}$

Given,

Purse ${}^{\prime }{1}^{\prime }$ contains $4$ copper coins and $3$ silver coins

Purse ${}^{\prime }{2}^{\prime }$ contains $6$ copper coins and $4$ silver coins

Probability of choosing each Purse is $\frac{1}{2}$.

Probability of choosing a copper coin $=$ (Probability of choosing a copper coin from Purse $1$ after you chose Purse $1$) $+$ (Probability of choosing a copper coin from Purse $2$ after you chose Purse $1$)

$=$ ((Probability of choosing Purse $1$) $\times$ (Probability of choosing a copper coin from Purse $1$)) $+$ ((Probability of choosing Purse $2$) $\times$ (Probability of choosing a copper coin from Purse $2$))

$=$ $(\frac{1}{2}$ $\times$ $\frac{4}{7})$ $+$ $(\frac{1}{2}$ $\times$ $\frac{6}{10})$

$=$ $\frac{2}{7}$ $+$ $\frac{3}{10}$

$=$ $\frac{41}{70}$

Therefore, the probability of choosing a copper coin from a purse which is chosen randomly is ${}^{\prime }{\frac{41}{70}}^{\prime }$.