Jim has to take two consecutive exams to get a certificate. The probability for him to pass the first exam is 0.7. If he pass the first exam, then the probability for him to pass the second exam will remain as 0.7, otherwise the probability for him to pass the second exam will be reduced to 0.35.

(a) A certificate can be only granted to the student who passed at least one exam. What's the probability for Jim to get a certificate ? (5 points)

(b) If Jim passed the second exam, what's the probability that he also passed the first exam ? (5 points)