in a room there are 3 married couples(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Homework Help: Probability question

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