With which group does the middle oxygen atom of an anhydride remain, on hydrolysis?
What I think is, the marked oxygen atom will stay with acetic acid because the carbon on the right side of the oxygen isotope has a slightly more &delta;+ charge than the carbon on the left due to the +I effect of methyl group attached to it. So, the marked oxygen should go with acetic acid instead of formic acid in the major product. 


  For the reaction the mechanism is usually tetrahedral. Only under acid catalysis does the SN1 mechanism occur and seldom even then.


The tetrahedral reaction mechanism of hydrolysis of anhydrides is similar to that for the hydrolysis of carboxylic esters which usually also proceeds through the tetrahedral mechanism.


  Of the eight mechanisms given by Ingold for ester hydrolysis, seven have actually been observed in hydrolysis of carboxylic esters. The one that has not been observed is the BAC1 mechanism. The most common mechanisms are the BAC2 for basic catalysis and the AAC2 for acid catalysis, that is, the two tetrahedral mechanisms. Both involve acyl-oxygen cleavage.


So considering the mechanisms for ester hydrolysis and anhydride hydrolysis to be similar, it can be proved that the extent of &delta;+ charge on the carbon being attacked does play a major role in deciding the rate of reaction.

For instance, the rate of hydrolysis for the following esters is in the order shown:

 

So I think this should be enough to prove what I stated in the very beginning of my answer. 



Source: Jerry March Organic Chemistry 6th edition, Organic chemistry by Paula Yurkanis Bruice.