Life gives probability lessons

Probability is a tough cookie to crack. Sometimes actual incidents make you curious and makes you wrack your brain and revise your probability lessons. Like the famous incident of Thomas Hardy spotting a taxi number while playing cards yesterday something happened which made me wonder and calculate the probability of what had transpired after the events took place. Let me replay the exciting turn of events !! There is a game called 5 3 2 played in 3 players who 10 get cards each After a game is over if you make more hands than your designated ones you get to choose that many cards from opponents cards next time So here is turn of events Game over I made 5 ( had to make 2) while my opponent made 2( had to make 5) so I got to pick 3 cards from opponents before next game starts

Game 2 begins cards are shuffled and opponent gets her 10 cards and gets a chance to see them if they want to arrange in any order and keep them down .

Chance 1. I call out a random number 3rd from top.

Opponent shows the card - Ace of spade Super excited. Gladly take it and return some ghatiya card back.

Chance 2. To make it fair opponent gets a chance to reshuffle so that there is a probability of the card you replaced to be called out hence going waste

I call out another random number 3rd from bottom this time . Ace of hearts this time. Oh my god what's happening. I gladly take it . Replace another ghatiya card of mine to opponent. Dancing with joy

Chance 3 opponents shuffles again. I call out another random number 4 the from top And any guesses what happened next?? Ace of diamond.

So to summarize my opponent had 3 aces and I extracted all of them ( rather legally looted ) all of them .

So what was the probability of the events that transpired? I think 3/10 * 2/10 * 1/10 = 6/100 . Less than 1% :) Is that correct? ( Because I already got the 4th ace with me in my original cards) . Also what will be the probability of getting 3 aces to one player?

And I so wish I was sitting in a casino in Las Vegas instead of comforts of my home:). I am glad my opponent was my aunt nahi to mera kya harsh hota:):)

PS: Random sunday musings to jot down:)