Does this PROVE “randomness”?

I was “randomly” selected to the same 160 person jury pool as an immediate member of my family.

Both of us were then, through further “randomness”, selected to the same 18 person jury. I told the Commissioner that I did not believe the selection process was reasonably random. He assured me that nothing like this had ever happened before. At which point, another member of the 18 person committee pointed to the woman next to him and said, “But this is my wife!”

“You see!” The Jury Commissioner triumphantly declared, “That *proves* that it’s random!”

My maths are a little rusty. Someone please explain…

Update:

160 out of a possible 600,000 - 900,000, depending on how they combine registered voters and people with driver's licenses.

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