5.1%. Less than half the chance of going undefeated (10.9%).
For completeness, odds of BYU losing # of games:
0 games 10.9%
1 games 31.8%
2 games 34.4%
3 games 17.8%
4+ games 5.1%
Losing 4+ isn't impossible, but I don't think it's quite as likely as you'd think.