Reaction of propylene oxide with ammonia or hydrazoic acid
In fact, these are at most chemoselective reactions, so there will probably be a mixture of all possible products.

Ignoring stereochemistry and assuming that we want to know the 'most probable' products, as far as I can tell the main difference is that $\ce{NH3}$ is a rather nucleophilic basic compound, whereas $\ce{HN3}$ is an acid and not very nucleophilic. We are not given the solvent, so we cannot know what side reactions can happen, or what solvation effects we have. So we may assume an 'inert' solvent is used.

Within these hypotheses, I'd say that $\ce{NH3}$ will react by $\mathrm{S_N}$2, attacking mostly on the least substituted side ($\ce{CH2}$), whereas $\ce{HN3}$ will protonate the oxygen first, and the opening by the azide anion will happen by $\mathrm{S_N}$1, i.e. attacking the most stable carbocation (the one with the positive charge on the most substituted carbon. So for me, the 'correct' answer would be 2.