A gene mutation is a permanent, heritable change in the DNA sequence of a single gene. These changes can alter the protein produced by the gene, potentially affecting an organism's traits or health.

Let N represent the dominant allele (unaffected) and n represent the recessive allele (cystic fibrosis).
Individual 9 and individual 10 are both unaffected (unshaded). However, they have an affected child (the first child between them, which is shaded). An affected child must have the genotype nn. For a child to have genotype nn, both parents must contribute an 'n' allele. Therefore, both individual 9 and individual 10 must be heterozygous carriers (Nn).

Parents: Nn $\times$ Nn
Gametes from Nn: N, n

• NN: Unaffected
• Nn: Unaffected (carrier)
• nn: Affected (cystic fibrosis)

From the Punnett square, there is 1 chance out of 4 for an offspring to have the genotype nn (cystic fibrosis).
Percentage chance = $\frac{1}{4} \times 100\% = 25\%$.

The percentage chance of them having a child with cystic fibrosis is $\boxed{25\%}$.