What should be the major product if 2-methylbuta-1,3-diene is treated with HBr ?

Consider the following possible products:

• Protonating carbon-1 yields the major product, if you note that when conjugation does NOT occur, you get a more stable carbocation.
• Protonating carbon-2 is a redundant way of getting to the major product, as it merely requires a 1,2-hydride shift that could have been avoided by protonating carbon-1 instead (molecules tend to be lazy and do the least work possible).
• Protonating carbon-3 would either yield a primary carbocation, or a secondary carbocation upon a 1,2-hydride shift. Either one is less stable than the tertiary carbocation from protonating carbon-1..
• Protonating carbon-4 is similarly as bad as carbon-3, even with the possibility for conjugation, as both yield primary or secondary carbocations to choose from, neither of which are great options.

  Any of the above products could happen, but the chosen products are expected to be most prominent.