Question

Urn-I contains 5 Red balls and 1 Blue ball,
Urn-II contains 2 Red balls and 4 Blue balls.
A fair die is tossed. If it results in an even number, balls are repeatedly withdrawn one at a time with replacement from urn-I. If it is an odd number, balls are repeatedly withdrawn one at a time with replacement from urn-II. Given that the first two draws both have resulted in a blue ball.
Conditional probability that the first two draws have resulted in blue balls given urn-II is used is

• A. $1/2$
• B. $4/9$
• C. $1/3$
• D. None

Answer 1

Answer: (B)

A: first two draws resulted in a blue ball.
$B_1\text{ : urn-I is used }P\left(B_1\right)=\frac{1}{2}$
$B_2\text{ : urn-II is used }P\left(B_2\right)=\frac{1}{2}$

$P\left(A/B_1\right)=\frac{1}{6}\cdot \frac{1}{6}=\frac{1}{36}$
$P\left(A/B_2\right)=\frac{4}{6}\cdot \frac{4}{6}=\frac{16}{36}=\frac{4}{9}$