In 1984 why does Winston believe that the hope of government overthrow lies in the hands of the proles?

At the very
beginning of chapter 7 in part 1, in the very first sentence,gives at least one of the reasons
that he believes the Proles are the only hope at successful revolution.  He mentions that they
are at least "85% of the population," so, they have numbers on their side.  Because
there are simply so many of them, they are the only ones that could be a large enough
"force to destroy the Party."  He said that rebellion was so difficult under the
watchful eye of Big Brother, but that the Proles who had more freedom from that ever-watchful
eye, could simply unite by "rising up and shaking themselves like a horse shaking off
flies."  So, by the mere fact that there are so very many of them, all they would have to
do is rebel, and their numbers alone would ensure success.

Secondly, they
aren't under the oppressive eye of Big Brother as intensely as non-Proles are, so they have more
freedom to move about and form a rebellion without being detected.  Because of this, they are
more free; Winston envies that freedom a bit, in fact, and wishes they would use it to overthrow
their oppressors.

Unfortunately, through very clever and insidious propaganda
and constant war-mongering to elicit a fury of patriotic devotion from the Proles, they never do
rebel. They are constantly pitched to a fever of rallying to the cause of the nation in wars
against its enemies, and the propaganda.  The masses are so controlled by this, in fact, that
the Party has no worries whatsoever about the Proles.  Their busy workschedules, their
exhaustion, and their being brainwashed into devotion to the cause, all keeps those masses in
check.

I hope that helped; good luck!