The integers form 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

Let the probability that 37 will in the first group be q and probability 89 will be in the second group be s. since quality and s are independent events,
p (q)=1/50
p (s)=1/50
thus p (QnS)=(1/50)(1/50)
=
=1/2500

therefore the probability that 37 & 89 will be in the same group is 1/2500