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# 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 A will not be selected?

$\begin{array}{1 1}(A)\;\large\frac{5}{9}\\(B)\;\large\frac{2}{9}\\(C)\;\large\frac{1}{9}\\(D)\;\text{None of these}\end{array}$

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:
A will not be selected
$\therefore P(A$ will not selected)=$1-P(A)=1-4x$
$\Rightarrow 1-\large\frac{4}{9}=\frac{5}{9}$
Hence (A) is the correct answer.