To find the probability that the hens lay more than two eggs, we need to sum the probabilities of the outcomes where the number of eggs is greater than two.
From the distribution table, these outcomes and their respective probabilities are:
- 3 eggs: [tex]\(P(X = 3) = 0.12\)[/tex]
- 4 eggs: [tex]\(P(X = 4) = 0.30\)[/tex]
- 5 eggs: [tex]\(P(X = 5) = 0.28\)[/tex]
- 6 eggs: [tex]\(P(X = 6) = 0.18\)[/tex]
To find the total probability for [tex]\(X\)[/tex] being greater than 2, we add these probabilities together:
[tex]\[
P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
\][/tex]
[tex]\[
P(X > 2) = 0.12 + 0.30 + 0.28 + 0.18
\][/tex]
Summing these values:
[tex]\[
P(X > 2) = 0.12 + 0.30 + 0.28 + 0.18 = 0.88
\][/tex]
Thus, the probability that the hens lay more than two eggs is:
[tex]\[
\boxed{0.88}
\][/tex]
