Sex-Lined Traits


Sorry to say, but you may have not read the title of this challenge correctly. It is not a challenge concerning Sex-LIKED Traits – It is, as it is written, SEX-LINKED TRAITS. Perhaps we'll take on that other challenge sometime in the future. Stay tuned.

Background: Normal humans have 23 pairs of analogous chromosomes. The chromosome pair associated with females is designated as XX and the pair associated with males is XY. Some genes on the X chromosome cause specific traits in the offspring (or children). Those traits, carried on the X chromosome are, at times, referred to as “Sex-Linked Traits.”

Color blindness, (most notably, red-green color blindness) is one such trait carried on the X chromosome. Your challenge is as follows:

Micah M. Millhouse, a middle-aged, modern thinking, member of the Mormon Church in the 1800's, had twelve wives. He was also red-green color blind and rumors circulated that he wasn't very particular about the looks of his wives either. 

The names of his wives are shown in the table below, along with the number of children each had, fathered by Micah. The children are separated by sex too. In case you're curious, Micah's much favored motto was,“Brigham Young – and keepem coming.” 

Wife name        Boys          Girls             Total Kids

Mary                   7                5                     12
Martina               6                8                     14
Margaret             5                5                     10
Melanie              4                 9                    13  
Melody               8                5                     13
Marsha               6                 6                    12  
Misha                 7                 7                    14 
Mabel                 2                 3                      5
Maddison           4                 5                      9
Macey                5                 3                      8
McKenzie          7                  1                     8
Madalyn             6                 3                      9

A female requires the color blind gene to be present on both X chromosomes in order for her to be color blind. (Xb Xb). A male only requires the gene to be on his one X chromosome (Xb Y) in order to become color blind.

We are assuming that none of Micah's wives are carrying the color blind gene. The diagram (genetic cross) of Micah and any of his wives would look like the one below, in bold print: (where the lower case “b” indicates the color blind gene on his X chromosome. 

[Xb Y x X X]

(Xb X), (X Y)

(Xb X), (X Y)

This yields the following possibilities in their children: Xb X,(a girl carrying the colorblind gene, but with normal vision), X Y, (a boy with normal vision, not carrying the trait), Xb X (another girl carrying the trait, but having normal vision), and X Y(a boy with normal vision, not carrying the trait).  

1. Based on the probability of inheriting a trait on Micha's X chromosome, how many of Micah's children will be red-green color blind? 2., How many sons will be affected and be colorblind? 3.,How many daughters will be color blind? 4., How many daughters might carry the trait but not be color blind themselves? 5., How many total grandchildren are most likely going to be color blind? 6., What % of his total grandchildren are most likely going to to be color blind? 7., What % of the male grandchildren most likely will be color blind? 8., When the male grandchildren grow up, what % of their children will probably be colorblind?