Question

Box $I$ contains $5$ red and $4$ blue balls, while box $II$ contains $4$ red and $2$ blue balls. A fair die is thrown. If it turns up a multiple of $3$, a ball is drawn from the box $I$ else a ball is drawn from box $II$. Find the probability of the event ball drawn is from the box $I$ if it is blue.

• A. $\frac{1}{6}$
• B. $\frac{15}{19}$
• C. $\frac{4}{19}$
• D. $\frac{10}{27}$

Answer 1

Answer: (D)

$\frac{10}{27}$

Box $I$ contains $:5$ red $+4$ blue

Box $II$ contains $:4$ red $+2$ blue

A ball is taken from Box $I$ if a multiple of $3$ comes up i.e, $3$ and $6.$

Ball is taken from Box $II$ when $1,2,4$ and $5$ turns up.

$\Rightarrow$ Event of picking up from Box $I=P\left(A_1\right)=\frac{2}{6}=\frac{1}{3}.$

$\Rightarrow$ Event of picking up from Box $II=P\left(A_2\right)=\frac{4}{6}=\frac{2}{3}.$

$\Rightarrow R=$ event of drawing a blue ball

$=P\left(A_1\right)P\left(\frac{R}{A_1}\right)+P\left(A_2\right)P\left({\frac{R}{A}}_2\right)$

$=\frac{1}{3}\times \frac{4}{9}+\frac{2}{3}\times \frac{2}{6}$

$=\frac{4}{27}+\frac{4}{18}$

$=\frac{10}{27}.$

Hence, the answer is $\frac{10}{27}.$