A package contains two machinery components: a regular one and a defective one. An industrial robot chooses a component at random and the chosen undergoes an electrical and a mechanical extreme test. If the component is non-defective, it has 50% chance to pass the electrical test and 50% chance to pass the mechanical test; for the non-defective component the outcomes of the electrical and the mechanical test are entirely unrelated. In contrast, the defective component fails both tests with absolute certainty (100% probability of mechanical & electrical failure if defective). Consider now the following events. A= Electrical test results in failure.
B= Mechanical test results in failure.
C= Non-defective (regular) component has been selected.
Find the following probability figures:
(a) P(AIC)
(b) P(BIC)
(c) P(Aâ©BIC)
(d) P(A)
(e) P(B), and
(f) P(Aâ©B)
(g) Consider the statement "A and B are NOT independent, but they are conditionally independent given C."
Explain in detail what it means and decide if it is true or false.