In the manufacturing of computer memory chips, company A produces one defective chip for every nine good chips. Let X be time to failure (in months) of chips. It is known that X is an exponential r.v. with parameter λ= 1/2 for a defective chip and λ= 1/10 with a good chip. Find the probability that a chip purchased randomly will fail before 

(a) six months of use;

(b) one year of use.