SOLUTION: 3 cards are drawn from 12 face cards of ordinary deck of 52 playing cards. Let x be the number of kings and y be the number of jacks. Find the joint probability distribution of x

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Question 569652: 3 cards are drawn from 12 face cards of ordinary deck of 52 playing cards. Let x be the number of kings and y be the number of jacks. Find the joint probability distribution of x and y.
Answer by AnlytcPhil(1807) About Me  (Show Source):
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3 cards are drawn from 12 face cards of ordinary deck of 52 playing cards. Let x be the number of kings and y be the number of jacks. Find the joint probability distribution of x and y.


J♥  Q♥  K♥ 
J♦  Q♦  K♦
J♠  Q♠  K♠
J♣  Q♣  K♣ 

The trinomial probability formula for non-negative integers x,y,z
where x+y+z = 3

   expr%283%21%2F%28x%21y%21z%21%29%29%281%2F3%29%5Ex%2A%281%2F3%29%5Ey%2A%281%2F3%29%5Ez 

or expr%286%2F%28x%21y%21z%213%5E%28x%2By%2Bz%29%29%29


Let z = the number of queens (i.e., non-jacks, non-kings)

Substitution in that formula gives the following trinomial
distribution:

x  y  z    p(x,y,z)
--------------------------------
0  0  3  1/27 = 0.03703704
0  1  2  3/27 = 0.11111111 = 1/9
0  2  1  3/27 = 0.11111111 = 1/9
0  3  0  1/27 = 0.03703703
1  0  2  3/27 = 0.11111111 = 1/9
1  1  1  6/27 = 0.22222222 = 2/9
1  2  0  3/27 = 0.11111111 = 1/9
2  0  1  3/27 = 0.11111111 = 1/9
2  1  0  3/27 = 0.11111111 = 1/9
3  0  0  1/27 = 0.03703703

Edwin