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*Off Topic* Probability question involving judicial split decision

Posted By: leobueno
Date: Thursday, 6 August 2026, at 5:13 p.m.

The 11th Circuit Court of appeals a couple of days ago issued an on opinion upholding the constitutionality of Florida's law banning children at drag shows (not the car racing variety). https://media.ca11.uscourts.gov/opinions/pub/files/202312160.enb.pdf

The decision was split, 8 judges in the majority and 5 in the minority.

Eight of the judges were appointed by Republican presidents; let's call them "Red" judges. The other five were appointed by Democratic presidents; call them "Blue" judges.

Let's assume that the issue in question was a very close one and that the judges are fair, so let's assume that the judges are fair coins.

If we were to toss the 13 coins, what is the probability that all 8 Red judges turned up in the majority and all 5 Blue judges turned up in the minority?

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