This is actually answered in Episode III novelization by Matthew Stover.
There's pretty much no difference to whether there are other Jedi aside from Luke and Leia and Yoda and Obi-Wan, according to Yoda, because the Old Jedi Order was inadequate to combat the New Model Sith as repersented by Sidious and Anakin. Old Jedi failed structurally, not because there weren't enough of them.
It came when the avatar of light resolved into the lineage of the Jedi; when the lineage of the Jedi refined into one single Jedi.
It came when Yoda found himself alone against the dark.
In that lightning-speared tornado of feet and fists and blades and bashing machines, his vision finally pierced the darkness that had clouded the Force.
Finally, he saw the truth.
This truth: that he, the avatar of light, Supreme Master of the Jedi Order, the fiercest, most implacable, most devastatingly powerful foe the darkness had ever known …
... just— didn’t— have it.
**He’d never had it. He had lost before he started.
He had lost before he was born.
The Sith had changed. The Sith had grown, had adapted, had invested a thousand years’ intensive study into every aspect of not only the Force but Jedi lore itself, in preparation for exactly this day. The Sith had remade themselves.
They had become new.
While the Jedi—
The Jedi had spent that same millennium training to re-fight the last war.
The new Sith could not be destroyed with a lightsaber; they could not be burned away by any torch of the Force. The brighter his light, the darker their shadow. How could one win a war against the dark, when war itself had become the dark’s own weapon?
Later, he meditates on that when waiting for Padme to give birth:
“Too old I was,” Yoda said. “Too rigid. Too arrogant to see that the old way is not the only way. These Jedi, I trained to become the Jedi who had trained me, long centuries ago—but those ancient Jedi, of a different time they were. Changed, has the galaxy. Changed, the Order did not—because let it change, I did not.”
And radio version of Star Wars had Obi-Wan acknowledge the same idea to Luke:
We are not altogether alone in the galaxy, you and I. But I doubt that we can rely on help from others of our kind.