Well
against the modern jet, the biplane would have no advantage whatsoever, he could turn on a sixpence compared to the modern jet who'd go wheeling past him at a comparatively massive velocity, for all the good that would do the biplane; by the time he'd gotten onto the jet's six o'clock, it would be in the next county. The biplane's manoeuvrability would no more help him against a modern jet than the A6M Zero's did against the faster, more powerfully-armed USN late-war fighters, once the USN had worked out the Zero's ace card.
Coming down to the speed of the biplane would be out of the question, it would be suicide, he'd likely drop out of the sky and even if he somehow didn't, he's playing the biplane at the biplane's game and consequently might still end up dropping out of the sky (what's this biplane armed with?)
I don't believe the biplane would ever be presented with a 'high chance' to defeat the modern jet.
I don't know enough about the modern stuff to offer a decent opinion but I'd hazard that the closing speed of the modern jet would be too much to take advantage of a 'boom and zoom' tactic; I don't know if the biplane's engine would generate enough heat for a missile lock or if there is another type of missile that the modern jet could call upon.
He could go guns-on and come in miles out from the target and just hope the biplane kept still for long enough but somehow I doubt that; the biplane would likely (assuming he'd kept his eye on the modern jet) use his manoeuvrability to suddenly present the jet with an impossible angle.
He could conduct a close-as-possible pass over the biplane on full afterburner, that would certainly screw his day up - he'd likely disintegrate.