I have a probability question I am stuck with. I’ll try and make this problem in plain English as possible – I'm sure it's simple Math but it's got me.
A new band is doing a group signing of their new album, each member of the group will be sat at desk signing individually.
There are 1000 people in the queue waiting for their signature.
The band consists of 4 people, PersonA, PersonB, PersonC, PersonD
PersonA is short on time and can only do 100 signatures. (10%)
PersonB has a little more time and do 200 signatures. (20%)
PersonC has all the time in the world and could do 600 signatures. (60%)
PersonD is also short on time and can only do 100 signatures. (10%)
The bouncer at the door sends each person in the queue to a member of the band, at random.
My question is what percentage would each band member need to be available to the bouncer, in order to hit their signing quota?
For example, if each band member was available 100% of the time, they would each sign 250 albums.
But I need to know what percentage PersonA needs to be available to sign 100 copies, no more and no less.
Most importantly I need the Mathematics behind it! So I can apply it to my actual problem.
Thank you any help or guidance.