Help with probabilities/odds for office pool

[accidentalaquarist]

Hi there

Been lurking and learning for a bit but this is my first time posting

We have an office pool going on and someone asked what the odds of winning were. And I hate to admit it but I had no idea.
So what better place than to ask here.
Our team has 7 people
categories are best sales, worst sales, and most improved sales for the quarter
I know that the odds of picking all three are 1:294 1/(7x6x7), but we've chosen to award the prize to anyone that can correctly predict 2 of the 3 categories instead of all 3. Presuming the challenge would be easier.
I have no idea how to work that one out. Theoretically the most improved can be either the best or worst salesperson.

Any help would be appreciated
AA

 

[Deleted member 4993]

Hi there

Been lurking and learning for a bit but this is my first time posting

We have an office pool going on and someone asked what the odds of winning were. And I hate to admit it but I had no idea.
So what better place than to ask here.
Our team has 7 people
categories are best sales, worst sales, and most improved sales for the quarter
I know that the odds of picking all three are 1:294 1/(7x6x7), but we've chosen to award the prize to anyone that can correctly predict 2 of the 3 categories instead of all 3. Presuming the challenge would be easier.
I have no idea how to work that one out. Theoretically the most improved can be either the best or worst salesperson.

Any help would be appreciated
AA

That would be true - if three different people were chosen for those three catagories.

You said that the best sales be also most-improved! (those better not be worst sales also - unless your company had 0 sales for years!!)

 

[accidentalaquarist]

That would be true - if three different people were chosen for those three catagories.

You said that the best sales be also most-improved! (those better not be worst sales also - unless your company had 0 sales for years!!)

Everyone's sales are up this quarter. So it is still possible, unlikely but possible for the worst salesperson to also be the most improved. Improvement is measured as a percentage over the individuals sales previously, not against team sales as a whole.

My brain keeps telling me the odds for getting 2 out of 3 right is 2/(7*7)+(7*7)+(7*6) or 1:70, but that just seems wrong to me for some reason.

AA