Probability involving members in a group

[Drunken Monkey]

There are six groups of four people each.
There is a deck of cards with aces, twos, threes, fours, fives, and sixes All other cards have been removed.
Groups are to be randomly assigned by each individual to pick a card and then depending upon what card they choose are assigned to a group (the aces are a group, twos are a group, ect.)

I was wondering the probability of two specific people being in the same group.

I think you just set it up like:

(4/24)*(3/23)*6

Which is the chance of person A picking a group multiplied by the chance person B picks the same group multiplied by the number of groups. . .

I am not all that confident in this answer, and think I am missing something. Thanks for any help.

[BruceZ]

[ QUOTE ]
There are six groups of four people each.
There is a deck of cards with aces, twos, threes, fours, fives, and sixes All other cards have been removed.
Groups are to be randomly assigned by each individual to pick a card and then depending upon what card they choose are assigned to a group (the aces are a group, twos are a group, ect.)

I was wondering the probability of two specific people being in the same group.

I think you just set it up like:

(4/24)*(3/23)*6

Which is the chance of person A picking a group multiplied by the chance person B picks the same group multiplied by the number of groups. . .

I am not all that confident in this answer, and think I am missing something. Thanks for any help.

[/ QUOTE ]

Correct. This is just 3/23. The first person can be in any group, and that leaves 3 cards for that group out of 23 total cards, so the probability that the other person is in the same group is 3/23.

[jay_shark]

Even easier .

Person A already has a number . There are three other players who share the same number and 23 players left .

3/23

[jay_shark]

Bruce beat me to it :P

[Siegmund]

OP left 28 cards in the deck, not 24 -- but I assume his intention was to remove seven ranks and leave six, in which case 3/23 will indeed be correct.

[BruceZ]

[ QUOTE ]
OP left 28 cards in the deck, not 24 -- but I assume his intention was to remove seven ranks and leave six, in which case 3/23 will indeed be correct.

[/ QUOTE ]

He said "There is a deck of cards with aces, twos, threes, fours, fives, and sixes". That's six ranks.

[Siegmund]

I read it as there's a deck with those ranks removed....

That is a fine paraphrase of why I only got a 790 on the math SAT [img]/images/graemlins/frown.gif[/img]

[Drunken Monkey]

Thanks for the help guys. I was pretty sure I was correct, but wanted to check to make sure.

As for the wording, there should have been a period somewhere in there. "There is a deck of cards with aces, twos, threes, fours, fives, and sixes. All other cards have been removed." Maybe that helps a little?