There are over twenty thousand objects orbiting in space. For a given object, let \(A\) be the event that the charred remains do hit the earth. Suppose experts, using their knowledge of the size and composition of the object as well as its re-entry angle, determine that \(P(A)=0.25\).

Next, let \(B\) be the event that your city is hit, given that charred remains reach the earth. The probability \(P(B \mid A)\) will depend on both the size of your city and its location relative to the current orbit of the object. Suppose that, the experts conclude that \(P(B \mid A)=\) 0.0002 .

(a) Find the probability that your city is hit with charred remains.

(b) Change \(P(B \mid A)\) to 0.0004 and repeat the calculation.