You have expressed that there is only one chance in all the possible combinations. You will have to rethink that.

Let's just start with mom and dad. Forget everyone else.

Address 1st letter to mom. It's right 1/2 or wrong 1/2

If it's right, then dad is 100%. If it's wrong, then dad is 0%

(1/2)*1 + (1/2)*0 = 1/2

This may seem to support your conlusion, however, you may be overlooking something with only two that is exposed by the question, What is the probability of getting exactly one of these right? If you miss one, you must miss a second. Misses come in at least pairs.

Let's just count grandparents. G1, G2, G3, G4. There are 24 ways to addresss these four. Let's assume the letters are in the first order listed. How many do we get for each possible prdering

G1G2G3G4 - 4

G1G2G4G3 - 2

G1G3G2G4 - 2

G1G3G4G2 - 1

G1G4G2G3 - 1

G1G4G3G2 - 2

G2G1G3G4 - 2

G2G1G4G3 - 0

G2G3G1G4 - 1

G2G3G4G1 - 0

G2G4G1G3 - 0

G2G4G3G1 - 1

G3G1G2G4 - 1

G3G1G4G2 - 0

G3G2G1G4 - 2

G3G2G4G1 - 1

G3G4G2G1 - 0

G3G4G1G2 - 0

G4G1G2G3 - 0

G4G1G3G2 - 1

G4G2G1G3 - 1

G4G2G3G1 - 2

G4G3G1G2 - 0

G4G3G2G1 - 0

If I have listed them correctly, we have p(4) = 1/24, p(3) = 0/24, p(2) = 6/24, p(1) = 8/24, p(0) = 9/24. I'm guessing this is not what you might have expected. In particular, 1/24 is the probability of getting them ALL correct.

Give it another go.