Quiz -- Wild Throw at First -- Timing Play?

Wild Throw at First -- Timing Play?

With one out, there are runners at third base (R3) and first base (R1). The batter (B1) grounds to the shortstop, who starts to turn a 6-4-3 double play. The throw to second base arrives in time to force out R1 at second base for the second out of the inning. However, the subsequent throw to first base is wild and pulls the first baseman off the base. The first baseman catches the throw and wheels around and tags B1 before B1 touches first base. B1 was tagged for the third out of the inning AFTER R3 touched home plate.

Does R3's run count since he scored before B1 was tagged out?

Call

In the play below, although B1 was tagged for the third out of the inning, B1 was tagged before he reached first base, so the out remains a force out. When the last out of the inning is a force out, no runs score (NF 9-1-1b) -- so no runs score on the play below.