I have a scenario where I am trying to understand how many different approaches I need to consider starting, to solve a given real-world problem in order to 'guarantee' that at least one of the approaches succeeds (i.e. that there is a solution). Suppose that each approach has a probability of (say) 90% of solving the problem. How many different approaches should be started so that there is a 'good chance' at least one succeeds? I realise 'guarantee' and 'good chance' are not ideal terminologies.
I think that this dice analogy is accurate:
Suppose I have n dice and these are all thrown once only in one shot. What is n for a reasonable probability that at least one dice will be a 6?