Dihybrid Crosses:

A cross of parental varieties differing in two characters.

A.  Mendel’s Second Law:  Independent Assortment

Alleles of different genes are assorted independently of one another during the formation of gametes:

Alleles of different genes from different chromosomes team up and are assorted together into newly formed gametes through meiosis.  Alleles of the same gene, from the pair of homologous chromosomes have to be separated druing this process (Mendel's First Law).

Punnett square:  A useful tool for showing all possible combinations of allele in offspring.  Each square represents an equally probable product of fertilization.
 

B.  Mendelian Inheritance and Rules of Probability
 

The probability scale ranges from 0 to 1.  An event that is certain to occur has a probability of 1, while an event that is certain not to occur has probability of 0.
 

The Rule of Multiplication:

To determine the chance that two or more independent events will occur together in some specific combination, we need to compute the probability for each independent event, then multiplying these individual probabilities to obtain the overall probabilities of these events occurring together.
 

EX.  A F1 plant is Pp, with purple color and a heterozygous genotype.  Purple to white
         color is dominant.

Question1: What is the probability that a particular F2 plant will have white flowers?
 
 
 

Question 2:  Dihybrid cross…
 
 

 
New Tools for Genetic Testing and Counseling:

Ex.  John and Carol are planning to have their first child and are seeking genetic counseling because of family histories of a lethal disease known to be recessively inherited.  John and Carol each had a brother who died of the disorder, so they want to determine the risk of their having a child with the disease…

1. From their brothers, both parents of John and Carol are both products of Aa and Aa.
a:  symbolizes the allele that causes this particular disease.
 

2. John and Carol are not homozygous recessive (aa), because they do not have the disease. Their genotypes are either AA or Aa.

3. Given a genotypic ratio of 1AA: 2Aa: 1aa for an Aa X Aa cross, John and Carol each have a 2/3 chance of being carriers.

4. Using the rule of multiplication, we can determine that the overall probability of their first born having the disorder is 2/3 (the chance that Carol is a carrier) multiplied by 2/3 (the chance that John is a carrier) multiplied by ¼ (the chance of two carriers having a child with the disease, aa genotype), which equals 1/9.