Draw cards from sample

ezbonanzo

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In a 30 card deck with 4 jokers, what are the odds of getting AT LEAST one joker in a 9 card hand? I forgot how to do this, it's been years since I've learned statistics. I know I have to find the odds of 1 - (no jokers)
 
In a 30 card deck with 4 jokers, what are the odds of getting AT LEAST one joker in a 9 card hand? I forgot how to do this, it's been years since I've learned statistics. I know I have to find the odds of 1 - (no jokers)

a hand dealt fresh off the shuffled randomly deck?

if so...

Pr[at least 1 joker] = 1 - Pr[no jokers in 9 cards]

Pr[card 1 isn't a joker] = 26/30
Pr[card 2 isn't a joker|card 1 wasn't a joker] = 25/29
etc.

Pr[card 9 isn't a joker|cards 1-8 weren't jokers] = 18/22

so this just forms a chain of conditional probabilities and

Pr[no jokers in 9 cards] = Product of all these 26/30 * 25/29 * ... * 18/22

subtract this from 1.

that's your probability

the value turns out to be 78.16% chance of at least 1 joker in freshly dealt 9 card hand.

I should add that this is the value for 9 cards dealt to a single player. If you are dealing 9 card hands to 2 or 3 players it will be different.
 
Last edited:
the value turns out to be 78.16% chance of no jokers in freshly dealt 9 card hand.

just to be sure, you meant "the value turns out to be 78.16% chance of [AT LEAST ONE joker] in freshly dealt 9 card hand."
thank you this solidifies my answer i found using matlab with sample simulation

goodsamples = 0;
for i=1:100000
y= datasample(hstone,9,'Replace',false);
if sum(y:))==2)>= 1
goodsamples = goodsamples + 1;
end
end

sum(y:))==2) is the number of 2's in the sample, and my matrix hstone is 1x30 with 4 entries of 2's
 
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