Probablity of two simultaneous events

[mtomagod]

Hello and thanks for reading my post, first time poster here.
This
My question is a little more complicated than the title implies but it goes as this:

There's a timeline of 60 recurring events. There's also two people who will manage the event at the time of occurrence. Given that person A managed 25% and person B managed 75% of the events on average, what is the chance person A will manage the event on the last event (60th) on the timeline?

Again, thanks for reading and I appreciate any responses.

 

[tkhunny]

Are the events independent? Why is the last event any different from the first event?
How long does it take to "manage the event"? Does an event ever have to wait to be managed?

Please show your work and share your thoughts.

 

[mtomagod]

Okay time is not a factor, consider the events managed instantaneously, the significance of the last event is that it starts the timeline over from the beginning and I'm just interested purely out of curiosity the actual probability.

I'm not sure how to show any work.

 

[tkhunny]

Well, the first question is the most important. You didn't answer that one.

 

[mtomagod]

Yes they are independent

 

[HallsofIvy]

Assuming the events are independent (tkhunny asked if they were independent and you didn't answer) then the probability of A managing any one event (and, in particular, the last) is 0.25 simply because we are "given that person A managed 25% of the events".

If that is not correct then there must be additional information you haven't given us.

 

[mtomagod]

I'm thinking the events are not independent then because that's not the answer I'm looking for.

In actuality the timeline will contain between 54 and 90 events and could restart at any point in that range. I thought by asking with just 60 it would make it easier. So sometimes the timeline will end at 61, sometimes 75, sometimes anywhere in there, I want to know what are the odds that the end of the timeline event and person a managing it will occur at the same time.

 

[tkhunny]

The fact that they are sequential is not relevant.

We agree to this:
A: 25%
B: 75%

One event comes along. A and B roll dice. 25% it goes to A and 75% it goes to B.

Here's the important part!

A second event comes along. How is the server for #2 selected? Do they roll the same dice, 25% vs. 75%? Does something else happen? Do they care if one or the other took on the first event? Does anyone remember who did the previous event? Since the event is handled instantaneously, there is no intrusive time factor. Either one could take on event #2. Who? How will you make the assignment?

 

[Steven G]

I agree with everyone here. Given the information that you gave us the chance on A managing any event is 25%. It does not matter which event number we are talking about--if it is random.
Just like you can flip an unfair coin (25% heads and 75% tails) and get 60 heads in a row, manager A can be called for all 60 events. If this is not the case then you need to explain how one gets chosen.

You stated I'm thinking the events are not independent then because that's not the answer I'm looking for. Do you have the answer to this problem? Can you tell us so we can have a chance to come up with a scenario that match the solution??