Question

The probability that f(1) is irrational,is $\frac{p}{q}$ (where p and q are coprime then) p+q is equal to

Answer 1

Consider the given function:

$f\left(x\right)=1$

$letx=0.1eq......\left(p\right)$

$multiplyingbothsideeq\left(p\right)by10.$

$x=0.1$

$10x=10\left(0.1\right)$

$10x=1eq......\left(q\right)$

$additionaleq\left(p\right)+\left(q\right)$

$[x=0.1]+[10x=1]$

$11x=1.1$

$x=\frac{1.1}{11}=0.1$

$sop+q=0.1$

Hence this is the answer.