In humans, the ABO blood type is under the control of autosomal multiple alleles. Red-green color blindness is a recessive X-linked trait. If two parents who are both type A and have normal vision produce a son who is color- blind and type \(0,\) what is the probability that their next child will be a female who has normal vision and is type \(0 ?\)

The only way for a child with type O blood to have parents with type A blood is if both parents carry the AO genotype (A is co-dominant with B, and O is recessive). Thus, both parents have an AO genotype for the blood type. As for the color vision, since both parents have normal vision and their son is color-blind, they must be carriers of the color-blind gene. The mother has XX chromosomes and the father has XY chromosomes. Their normal vision indicates that they carry one normal vision allele and one color-blind allele. So, the genotype of the mother is X^AX^a, and the genotype of the father is X^AY.

Now, we will set up two separate Punnett squares - one for blood type and one for color vision. This will help us determine the probability of the child having the desired traits. For blood type, we need to determine the offspring's genotypes from parents with AO genotypes: ``` __A_|__O_| A| AA | AO | -------- O| OA | OO | -------- ``` For color vision, we need to determine the offspring's genotypes from a mother with the X^AX^a genotype and a father with the X^AY genotype: ``` __X^A_|__Y__| X^A|X^AX^A|X^AY| --------- X^a|X^AX^a|X^aY| --------- ```

Now, we will determine the probability of each desired trait for the next child: 1. Probability of type O blood (OO genotype): From the blood type Punnett square, the probability of having an OO genotype is 1/4 (there is one OO square out of the four possible outcomes). 2. Probability of the child being female (having XX chromosomes): From the color vision Punnett square, the probability of having XX chromosomes is 1/2 (two out of the four possible outcomes have XX chromosomes). 3. Probability of having normal vision (non-color-blind, X^AX^A or X^AX^a genotype): From the color vision Punnett square, the probability of having normal vision is 3/4 (three out of the four possible outcomes represent normal vision, counting both X^AX^A and X^AX^a genotypes).

To determine the overall probability of the next child being a female with normal vision and type O blood, we need to multiply the individual probabilities: Overall Probability = (Probability of type O blood) x (Probability of being female) x (Probability of having normal vision) = (1/4) * (1/2) * (3/4). Overall Probability = (1/4) * (1/2) * (3/4) = 3/32 Thus, the probability of their next child being a female with normal vision and type O blood is 3/32.