Question

One bag contains 3 white balls, 7 red balls and 15 black balls. Another bag contains 10 white balls, 6 red balls and 9 black balls. One ball is taken from each bag. What is the probability that both the balls will be of the same colour?

• A. $207/625$
• B. $191/625$
• C. $23/625$
• D. $227/625$

Answer 1

Answer: (A)

$207/625$

Bag $I=$ $3$ White $+$ $7$ Red $+$ $15$ Black

Bag $II=$ $10$ White $+$ $6$ Red $+$ $9$ Black

Each beg contains total of $25$ balls.

There are three cases for selection of a particular ball :

$1.$ White ball from Bag $I$ and Bag $II=\frac{3}{25}\times \frac{10}{25}$

$2.$ Red ball from Bag $I$ and Bag $II=\frac{7}{25}\times \frac{6}{25}$

$3.$ Black ball from Bag $I$ and Bag $II=\frac{15}{25}\times \frac{9}{25}$

$\therefore$ Total probability $=\frac{30}{625}+\frac{42}{625}+\frac{135}{25}=\frac{207}{625}.$

Hence, the answer is $\frac{207}{625}.$