this is my first Cross Validated post!
I am trying to figure out how to choose between two different sequences to obtain a desired outcome. This is the best way I can think of to desribe the situation:
In option 1 there are two events. In the first event there is a 5% chance to obtain the reward. In the second event there is a 9% chance to obtain the reward. You can get the reward from each event.
In option 2, there are two events. In the first event there is a 0% chance of the reward. In the second event there is a 12% chance of getting the reward.
Which sequence has the highest total probability of getting the reward and why?
I am a complete neophyte when it comes to statistics, so I am hoping to start learning here! Thank you for your help!
Edit: In each Option, the sequence of event A and event B always happen. Each take approximately 5 minutes each. At the end of each event, regardless of the Option, a random number generator generates a "reward"; the probability that it is the desired "reward" are those stated above.
Assuming we get past these communication issues, I would be curious how difference in the length of each option would affect the outcome.
Are there other data needed? Thank you!
Edit 2: Ok, I've tried to capture this in a picture, because that's how I'm thinking about the situation and clearly my attempts to write it out have not been successful.
Each rectangular block is what I've been referring to as an "event". Every event, once you are on a path happens 100% of the time; their occurrence is an intrinsic part of the option.
I am assuming that with Option B, the chance of getting the reward really is just 12.2% of every time I select Option B. For Option A, with the two options, I do not understand how to combine them together into a single "number" that represents that Option's potential to result in 1 (or possibly 2) rewards, so that I can compare it against taking Option B. I am assuming that there is a statistical method that will allow me to make an apples to apples comparison of the two Options so that I can understand which would be better to take (where better = highest likelihood of reward).
Is that any better?