2022 CJC J2 MYE Q6

A student attempts three papers for an examination. The probability that he passes the first paper is \(0.7\). If he passes a paper, the probability of him passing the next paper increases by \(0.05\). If he fails a paper, the probability of him passing the next paper is \(0.7\).

1. Draw a tree diagram to represent this situation, showing all possible outcomes.[3]
2. Find the probability that the student passes at least two of the three papers.[2]
3. Find the probability that the student passes his third paper, given that he passed only once in either the first paper or the second paper.[3]