Wow. This thread sure went south in a hurry. If you're purely interested in someone giving you the answer, then, yes, you'll need to look elsewhere as we do not provide that here. But I'd be wary of such "cheetz" sites as most of them are really scammers, so use a credit card and be prepared to cancel it immediately. If, on the other hand, you're interested in learning how to solve not just this problem, but also others like it, we can help you with that. We've found it generally works best to ask the students leading questions to encourage them to think about the problem, to think about the process, and come to understand what they're doing and why it works.
That said, here's another way you might think about this problem. Perhaps this one will "click" with you. Because you're interested in the probability of at least one success, that effectively means you can stop after winning any one of the four rounds. So, you know you'll win the first round 1/6 of the time. But what happens the other 5/6 of the time? Well, you have to then play round two. Given that you win round two 1/3 (2/6) of the time and you only even reach round two 5/6 of the time, what's the probability of winning on round 2? What's the probability of not winning on round 2? Then proceed to round three. You have a 1/2 (3/6) chance of winning and a (what chance?) of reaching round three. Finally, proceed to round 4. Where does this process take you?
