Question

${}^{\prime }{A}^{\prime }$ and ${}^{\prime }{B}^{\prime }$ each have a bag that contains one ball of each of the colours blue, green, orange, red and violet. ${}^{\prime }{A}^{\prime }$ randomly selects one ball from his bag and puts it into B's bag. ${}^{\prime }{B}^{\prime }$ then randomly selects one ball from his bag and puts it into $A^{\prime }s$ bag. The probability that after this process the contents of the two bags are the same, is

• A. $1/6$
• B. $1/5$
• C. $1/3$
• D. $1/2$

Answer 1

The correct option is B $1/5$

Given, In two bags, each contains 1 blue, 1 orange, 1 green, 1 red and 1 violet.
The total no. of ways of placing 1 ball from first bag into the second bag$=$${}^5{C}_1$
The total no. of ways of placing 1 ball from second bag into the first bag after 1 ball kept in second bag=${}^6{C}_1$
$\therefore$ The total no.of ways to happen for this process=${}^5{C}_1{\ast }^6{C}_1=30ways$
The number of ways even after the above process, the bags remain unchanged$=$${}^5{C}_1\ast 2C_1=10ways$
${}^5{C}_1\to$ number of wways selecting one colour from 1st bag
${}^2{C}_1\to$ number of ways selecting same colour from 2nd bag which have been initially selected in the first bag
$\therefore$ The Required probability$=\frac{10}{30}=\frac{1}{3}$