The integers from 1 to 100 are randomly separated into two groups of 50 integers each. What is the probability that 37 and 89 are in the same group?

Question

anonymous · Answer

1/2

tkhunny · Answer

Are 37 and 89 special?  What the probability that any 2 are in the same group?

anonymous · Answer

It is not 1/2. It is 49/99.

anonymous · Answer

@BangkokGarrett Can you explain?

anonymous · Answer

so it is more likely that they are in the same batch than not?

anonymous · Answer

37 will be randomly placed into one of the 2 groups. That leaves 49 unfilled spots in 37's group and 50 unfilled spots in the other group. Of those 99 unfilled slots 49 are in 37's group. 89 is equally likely to fall into any of these spots.

anonymous · Answer

i mean "less likely" 
seems odd

anonymous · Answer

No, it's more likely they are in different slots.

anonymous · Answer

Oh I see, thanks!

anonymous · Answer

if you do it that way you have to take in to account that there are two possible sets for 37 to be in

anonymous · Answer

Simplify it and just look at the integers 1,2,3,4
What are the possible groupings?
12 .. 34
13 .. 24
14 .. 23
23 .. 14
24 .. 13
34 .. 12
1 and 2 are not together in 1/2 of those are they? Only in 1/6th of them.

anonymous · Answer

yes, you are right