Using probability theory, the joint success depends upon both the modules success and
the integration success. As all these things happen independently, the total success is
the product of their probabilities.
P(UNIT) X P(INTEG.)= 0.9 X 0.9 = 0.81
also if we consider this line
"Unit testing is independent and can be performed at any point of SDLC. On the other hand, integration testing is conducted after unit testing is completed and system testing begins"
i.e. conditional probability, they should've mentioned P(integration|unit) parameter for calculating P(unit & integration).
the source must have mentioned the wrong answer.