Question

Two urns $A$ and $B$ contain marbles. Urn $A$ holds $12$ black marbles and $4$ white marbles. Urn $B$ contains $6$ black marbles and $5$ white marbles. $A$ marble is chosen at random from Urn $A$ and placed in Urn $B$. The probability that a marble then chosen from Urn $B$ is black, is

• A. $\frac{9}{16}$
• B. $\frac{6}{11}$
• C. $\frac{5}{11}$
• D. $\frac{13}{24}$

Answer 1

Answer: (A)

$E_1$ : Marble transferred from $A$ to $B$ is black.
$E_2$ : Marble transferred from $A$ to $B$ is white.
$E$ : Marble drawn from $B$ is black.

$P(E)=P\left(E_1\right)\cdot P\left(\frac{E}{E_1}\right)+P\left(E_2\right)\cdot P\left(\frac{E}{E_2}\right)$
$=\frac{12}{16}\cdot \frac{7}{12}+\frac{4}{16}\cdot \frac{6}{12}=\frac{9}{16}.$