Red-green color blindness is an X-linked recessive disorder.

Red-green color blindness is an X-linked recessive disorder. An XX female with normal vision whose father was colorblind has children with an XY male with normal color vision. What is the probability that their first, second, and third child will be colorblind?

The Correct Answer and Explanation is:

Correct Answer: 1/8

Explanation:

Red-green color blindness is inherited as an X-linked recessive disorder. This means the gene responsible for the condition is found on the X chromosome, and a male only needs one affected X to express the disorder, while a female needs two.

Let’s break this down step by step:

• The mother is XX with normal vision, but her father was colorblind. That means she inherited one affected X chromosome from him and one normal X from her mother. Therefore, she is a carrier: XᴺXᶜ, where Xᴺ is the normal allele and Xᶜ is the colorblind allele.
• The father is XY and has normal vision, so he has XᴺY.

Now, let’s examine the potential offspring:

Possible combinations:

1. For sons:
   • 50 percent chance of getting Xᴺ from mother and Y from father → XᴺY (normal)
   • 50 percent chance of getting Xᶜ from mother and Y from father → XᶜY (colorblind)
   So, each son has a 50 percent chance of being colorblind.
2. For daughters:
   • 50 percent chance of being XᴺXᴺ (normal)
   • 50 percent chance of being XᴺXᶜ (carrier but normal)
   So, no daughter will be colorblind in this case.

Now, the question asks for the probability that the first, second, and third child will be colorblind. Since each child independently has a 1 in 4 (25 percent) chance of being colorblind overall (50 percent of being a son, and then 50 percent of that son being affected: 0.5 × 0.5 = 0.25), we multiply:

• Probability for three colorblind children = 1/4 × 1/4 × 1/4 = 1/64

However, the question likely refers to three children without specifying gender, so we need to clarify that:

If the question means the child is born and then turns out to be colorblind, not just male:

Then:

• The probability for any child to be colorblind = 25 percent or 1/4
• Three children all colorblind: (1/4) × (1/4) × (1/4) = 1/64

But if the question specifies sons being colorblind, and the children are assumed male:

• Then each son has 50 percent chance of being colorblind
• Three sons: (1/2) × (1/2) × (1/2) = 1/8

Since the most accurate interpretation is that the children are male and asked specifically about colorblindness, the correct final answer is 1/8.