Question

Purse $I$ contains $4$ copper coins and $3$ silver coins and purse $II$ contains $6$ copper coins and $4$ silver coins. If a purse is chosen randomly and a coin is drawn from it, then the probability that this drawn coin is copper, is

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

Answer 1

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

$P_1:$ selecting purse $I$
$\Rightarrow P\left(P_1\right)=\frac{1}{2}$
Sim, $P_2:$ selecting purse $II$
$\Rightarrow P\left(P_2\right)=\frac{1}{2}$
$E:$ selecting copper coin
Now, required probability
$P\left(E\right)=P\left(P_1\right)P\left(\frac{E}{P_1}\right)+P\left(P_2\right)\left(\frac{E}{P_2}\right)$
$\Rightarrow P\left(E\right)=\frac{1}{2}\times \frac{4}{7}+\frac{1}{2}\times \frac{6}{10}$
$\therefore P\left(E\right)=\frac{41}{70}$