A fetal test of genetic material is being developed to deter

A fetal test of genetic material is being developed to determine the eye color of a baby. The percentage of humans having brown eyes in given in D1, and the percentage having blue eyes is given in D2. Of those with brown eyes, the percentage carrying a certain genetic marker is given in D3, while of those with blue eyes, the percentage carrying the same marker is given in D4. If a person carries the marker, what is the probability that they will have blue eyes? (Enter your value in cell D6.)

Now, use these probabilities to design a simulation so that column A simulates one thousand people sampled at random for eye color and the marker. That is, enter one of “bm” (for brown without marker), “bM” (for brown with marker), “Bm” (for blue without marker), “BM” (for blue with marker) in each of A1:A1000. Check the validity of your model by giving in G1 the percentage of the simulation with “b”, in G2 the percentage of the simulation with “B”, in G3 the percentage of “b” the simulation with “M”, in G4 the percentage of “B” with “M”. Finally, in G6 give the proportion of “M” with “B”.

percentage of brown eyes: percentage of blue eyes: percentage of marker for brown eyed percentage of marker for blue eyed: probability of blues eyes for marker: 82 percentage of b 18 percentage of B 10 percentage of M among b 89 percentage of M among B: proportion of B among M

Solution

We have the proportion of brown eyes 0.82 .

The proportion of Blue eyes 0.18.

The proportion of marker for brown eyed 0.1

The proportion of marker for blue eyed = 0.89.

Now we are to calculate the probability of having a blue eye when they are known to have marker,

P( Blue eye given Marker ) = P( Blue eye and marker) / P( Marker) = (0.89*0.18)/[P(Marker and Brown eye) + P( Marker and Blue eye)] = (0.89*0.18)/[(0.82*0.1) + (0.89*0.18)] = 0.1602/(0.082 + 0.1602) = 0.6614 .

The following table shows the proportion of the respective classes.

class           Prop.

bM              0.075

bm              0.745

BM             0.163

Bm             0.017

Total           1.000

Therefore, Percentage of b = 7.5+74.5 = 82%

Percentage of B = 18%

Percentage of M among b = (0.075/0.82)*100 = 0.09*100 = 9% .

Percentage of M among B = (0.163/0.18)*100 = 0.91*100 = 91% .

The proportion of B among M = (0.163)/(0.163+0.075) = 0.6848.