problem:After masks are produced by the factory, they appear in a test center, where they are tested for defects. Historically, only 10% of masks get a positive test result (meaning they are defective).
Let $T_1$= number of masks tested until first positive result, $T_2$= number of masks tested until second positive result.
Find $P(T_2=r\,∣\,T_1=n)$ and then, using it, $P(T_2=r)$.
I know $P(T_2=r\,∣\,T_1=n)=0.9^{r-1}\times 0.1$ , but don't know how to find $P(T_2=r)$.