I played a card game with my fam where we are in 2 teams of 2 (4 of us total). Each player gets a hand of 7 cards from the 52 deck and between myself and my partner we needed a king OR an ace. In a total of 3 hands each (so 6 hands total between me and my partner) neither of us got a king OR an ace. This seems very unlikely to me. I can't do the maths on it so I need some help and an explanation of how to do it (dumbed down please) would be appreciated!
2026-03-29 20:20:08.1774815608
card game chances
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We need to choose $14$ cards from the $52-8=44$ non-king-non-aces to make such an "unlucky" hand. All possible hands may be generated by taking $14$ out of $52$. Thus the probability in the blockquote above is $$\binom{44}{14}/\binom{52}{14}=0.0649847\dots$$ To get the probability that the above happens for three rounds, cube the one-round result. You get $$0.000274431\dots$$ or $0.027\%$.