Can anyone please explain me what us happening in part 1 of this question, we should be looking at the probability of changing the auditor, then why are we taking 0.8?
Try not to think it terms of "changing auditors", but rather "not changing auditors" (i.e. staying with Auditor A). The question tells us that the country must have a minimum of two annual audits with a firm. With no intention of insulting your intelligence let's write this as 1 + 1. Come the 3rd audit (the first time the country has a chance to change auditors), what's the probability that the country does not change auditor? P(A) = 0.8 The probability of choosing A for 2 years more? P(A and A) = 0.8^2 And so on...We may stay with Auditor A forever. What we end up with is a geometric series (the part in brackets - and now you see why I wrote 2 as 1 + 1): 1 + (1 + 0.8 + 0.8^2 + 0.8^3 + ... ) I presume you remember how to find the sum of an infinite geometric series. This is the last step of the solution in the examiners report.
