Need help determining percentage please?

#1
Ok didn’t know where to go for help on this. We play a card game called Pedro at our firestation. 2 teams of 2 people. if all Players have 9 cards each, and one player does not have a black 5. What is the percentage that his teamate will have a black 5 over the other 2 players. Would it be a 50/50 chance that out of the 27 cards his teammate will have a black 5 in his 9 cards or the other team will have it in their 18 cards.

not sure I explained it right
thanks
 
#2
The chance his teammate will have at least one of the 2 black 5's, given that one player does not = 1 - the chance his teammate will not have either black 5 = 1 - { choose(41,9)/choose(43,9) } = 40% approx., hopefully I got that right, seems too high, should match 'hypergeometric' probability formulas. For the 2 adversaries, the chance that between them of having at least one of the black 5's will be 1 - { choose(41,18)/choose(43,18) }, about 70%, so roughly twice as likely, not quite.

feel free to forward some chili recipes, less than 4 alarms...
 
#3
27 unknown cards dealt

9 known dealt cards have no black 5

16 unknown cards not dealt

Of the 43 unknown cards:

P b5 =2/43

P 1 b5 in unknown 27 dealt cards = 2/43 * 27/43

P 2 b5 in unknown 27 dealt cards = 2 * 2/43 * 27/43

P 1 b5 in 16 not dealt cards = 2/43 * 16/43

P 2 b5 in 16 not dealt cards = 2 * 2/43 * 16/43

P 1 b5 in unknown 27 cards and 1 b5 in 16 not dealt cards =

(P 1 b5 in unknown 27 dealt cards = 2/43 * 27/43) + (P 1 b5 in 16 not dealt cards = 2/43 * 16/43)

I think, and I could very well be wrong, that a condition must be attached to any Px;

Ex: P partner has 2 b5 requires that 2 other team members and 16 not dealt cards have no b5 .

There are MANY possible ways that partner has 2 b5.
 
#4
i cant really tell if it is agreeing or disagreeing with my answer. either way looks like now chili recipes forth-coming so im foldin', callin it a day on this one..
 
#5
"What is the percentage that his teamate will have a black 5 over the other 2 players." The probability that the teammate has a black 5 and the other 2 players do not is 1/3, 33%, .33. When will the chili arrive?
joe b.