Simple problem on conditional geometric probability The occurrence of the event $A$ is equally likely in every moment of the interval $[0, T]$. The probability of event $A$ occurring at all in this interval is $p$. Given that $A$ hasn't occurred in the interval $[0,t]$ what's the probability that $A$ will occur in $[t, T]$?
I am getting a different answer than the one given in the book. I wonder which one is correct. My answer is
$\dfrac{Tp-tp}{T-pt}$
The book's answer is my answer divided by $p$. 

We have $$\Pr(A\in (0,T)\mid A\not\in(0,t))=\frac{\Pr(A\in (t,T))}{\Pr(A\not\in(0,t)}.$$
The top probability is $p\frac{T-t}{T}$ and the bottom is $1-p\frac{t}{T}$; rearranging this gives the same answer you have.
