On a winter’s evening, two couples, Jack and Jill, Willy and Lola, went to the famous French restaurant Chez Clouseau in New York to delight their taste buds with a three star Michelin cuisine.
After entering the plush lobby, they had to check their coats in the wardrobe, which was attended by Molly, a distrait blonde.
“Welcome to Chez Clouseau, y’all. Please check in your coats, y’all” said Molly, gracefully extending her arm, fingers glittering with rings.
The couples obliged and were handed four numbered plastic cards engraved with the Chez Clouseau logo, an inscripton with two crossed red wine bottles on a fleur-de-lis background, upon which they were led at a brisk but elegant pace by the maitre d’ to their table.
After dining at a tastefully set table with dishes crisscrossed in an artistically random fashion with sprayed-on green stripes – just missing some small stacks of colorful tidbits – drinking expensive vintage Bordeaux wine, and then paying the exorbitant bill, the couples returned in a financially decimated and bewildered state to the wardrobe to at least recover their coats.
“Our coats please,” commanded Jack, handing the plastic cards to Molly so she could connect the right owner with the right coat.
“Thank you mister,” beamed Molly with a charming smile. Just then a handsome French waiter passed by with a tray holding several full wine glasses, and Molly’s eyes glued onto and followed the garçon, dropping the plastic cards, which fell helter-skelter in a random fashion on the floor behind the wardrobe counter.
“Oops,” she blushed all flustered, “Really, how could this all have happened, y’all.”
She quickly checked the numbers on the plastic cards and handed Jack and Jill and Herman and Lola the coats corresponding to the numbers on the cards and the coat rack.
As the ordered taxi was beeping loudly outside, the two couples grabbed the coats given to them and raced out the door in a rush to leave. Molly didn’t get a tip.
What is the probability that at least one of the four received their own coat on checking this in the taxi? And the probability that one of the couples both received their own coat? That both couples received their respective own coats?