Calculating Probability of Correct Guesses in 3 Married Couples

[Dell]

in a room there are 3 married couples
somebody guesses which of the men are married to which of the women.
X=number of correct guesses.

find E(x), var(x)

i tried the following

X=0 (no correct guesses)
P(X)=2/3*2/3*2/3=8/27

X=1 (one correct guess)
P(X)=2/3*2/3*1/3=4/27

X=2 (two correct guesses)
P(X)=2/3*1/3*1/3=2/27

X=1 (three correct guesses)
P(X)=1/3*1/3*1/3=1/27


BUT the total
P(X=0) + P(X=1) + P(X=2) + P(X=3) does not come to 1
(8+4+2+1)/27=5/9

where am i going wrong? there are only 3 couples so he could not guess more that 3 correct couples.
the probability of guessing a correct couple is 1 in 3

 

[Dick]

You are assuming the probability of a guess being correct is independent of previous guesses. That's not true. For example, there is no chance at all of getting two guesses correct and the third one wrong.