Assignment:
A bicycle plant runs two assembly lines, A and B. 96.3% of line A's products pass instruction, while only 92.1% of line B's products pass inspection, and 70% of the factory's bikes come off assembly line A.
a) What is the probability that a randomly selected bike passed inspection?
b) What is the probability that a randomly selected bike that did not pass inspection came from assembly line B?
Provide complete and step by step solution for the question and show calculations and use formulas.