It's the awoken part. She's sleeping beauty, and keeps on sleeping if you don't wake her up. The important part is that she only awakes on Mondays or Tuesdays

It's the awoken part. She's sleeping beauty, and keeps on sleeping if you don't wake her up. The important part is that she only awakes on Mondays or Tuesdays when you actively wake her up. So since she's twice as likely to be woken up when the coin showed tails the conditional probability from her perspective for tails is higher. I don't think the shows or showed part makes the big difference here assuming you left the coin as is after throwing it. It's the conditional probability part. But they did try to explain it in a mysterious click-bait way. I'm pretty sure there aren't many Mathematicians kept awake by this at night.