For three autosomal dominant genes, what is the probability that a cross between two heterozygotes (i. e. AaBbCc x AaBbCc) will produce an offspring with the dominant trait for all genes?

27/64 or 0.421

Explanation:

When AaBbCC X AaBbCc:

A_B_C_ = 27

aaB_C_ = 9

A_bbC_ = 9

A_B_cc = 9

aabbC_ = 3

A_bbcc = 3

aaB_cc = 3

aabbcc = 1

Out of the total 64 offspring, 27 will have at least one dominant allele for each of the three genes hence these 27 offspring will show dominant trait for all genes. So the probability of producing a dominant trait for all genes will be 27/64 or 0.421