To solve this problem, we need to analyze the genetic inheritance of color blindness, which is a sex-linked recessive trait.$\newline \bullet$Color blindness is carried on the X chromosome. A female has two X chromosomes (XX), while a male has one X and one Y chromosome (XY).$\newline \bullet$A color-blind female has the genotype$X^{c}. X^{c},$ where $X^{c}$ represents the X chromosome carrying the color blindness allele.$\newline \bullet$A man whose mother was color-blind must have inherited the$X^{c}$ chromosome from her, so his genotype is $X^{c}Y. \newline$Let's determine the possible genotypes of their progeny:$\newline \bullet$The female can only pass on an $X^{c}$ chromosome.$\newline \bullet$The male can pass on either an $X^{c}$ or a Y chromosome.$\newline$The possible combinations are:$\newline \bullet X^{c}X^{c}$(female, color-blind)$\newline \bullet {X^{c}}Y$(male, color-blind)$\newline$All progeny will inherit the color blindness allele, resulting in 100% of the children being color-blind.$\newline$Therefore, the correct answer is Option 4: 100%.