# Four candidates A,B,C,D have applied for the assignment to coach a school cricket team.If A is twice as likely to be selected as B,and B and C are given about the same chance of being selected,while C is twice as likely to be selected as D,what are the probabilities that C will be selected?

$\begin{array}{1 1}(A)\;\large\frac{3}{7}\\(B)\;\large\frac{2}{9}\\(C)\;\large\frac{1}{9}\\(D)\;\text{None of these}\end{array}$

Step 1:
Let the probability of D selected be $'x'$
$\therefore P(D)=x$
$P(C)=2x$
$P(B)=2x$
$P(A)=4x$
$P(A)+P(B)+P(C)+P(D)=1$
Sum of all probabilities =1
$\therefore 4x+2x+2x+x=1$
$9x=1$
$x=\large\frac{1}{9}$
Step 2:
C will be selected
$\therefore P$(C selected)=$2x$
$\Rightarrow 2\times \large\frac{1}{9}=\frac{2}{9}$
Hence (B) is the correct answer.