Probability problem

[PuzzleRocks]

Can anyone help? It's driving me mad.


A company consist of 32 experts

There are always 16 teams (2 experts) on each shift

Team consists of 1 team leader and 1 team member

There is always an equal number of experts on their 1st 2nd 3rd 4th 5th shift


What is the probability of someone on their 1st 2nd 3rd shift being led by someone on their 3rd or 4th shift?

TIA

[PuzzleRocks]

Anyone?

[mranchovy]

32 is not divisible by 5 so there cannot be an equal number on each shift; I will assume that there are 30 experts in 15 teams, that there are an equal number of leaders and members and that the shift patterns are rotated in an unbiased way (this may not be simple to arrange) or allocated randomly so that over time there is no bias.

Now, a member on their 1st (or 2nd or 3rd) shift is equally likely to be led by a leader on any shift 1 to 5, so each has a 20% chance. The chance of a leader on their 3rd or 4th shift is therefore 40%.

[PuzzleRocks]

That's what I was getting hung up on. The 5 into 32. Thanks for your help.

[mranchovy]

... even though there can't be an eqal number on each shift, as long as the shifts are rotated so that everyone does an equal number of each shift and there is no link between the shifts (as I say, this is very difficult to achieve in practice), the chance is still 40%.