NOTE: Before completing this worksheet, you should read the article, "Applications of Statistics and Probability to Genetics" by Hunter Ballew, taken from the NCTM Yearbook, Teaching Statistics and Probability (1981).

Gregor Mendel, an Austrian monk (1822-1884) was the first to allow for randomness in the study of genetics. In an effort to understand how characteristics were transmitted from one generation to the next in plants, he counted the number of occurrences of various characteristics. Mendel found that the flower color in certain pea plants obeyed this rule: Pure red crossed with pure white produces red. Now the red offspring received from its parents genes for both red (R) and white (W), but in this case red is dominant and white is recessive, so the offspring exhibits the color red. However, the offspring still carries both genes, and when two such offspring are crossed, several things can happen in the third generation as shown below in the table, which is called a Punnet square:
 
 

The body of the table shows the possible combinations of genes. Recalling that red is dominant over the recessive white character (one or more red genes leads to a red flowered offspring), find

1.    The probability of getting a red offspring in the third generation.

2.    The probability of getting a white offspring in the third generation.
 

Mendel found no dominance in snapdragons, with one red gene and white producing pink flowered offspring. These second generation pinks, however, will carry one red and one white gene, and when they are crossed, the next generation still yields the Punnet square shown above. Find

3.    The probability of getting a red offspring in the third generation.

4.    The probability of getting a pink offspring in the third generation.

5.    The probability of getting a white offspring in the third generation.

6.    Construct a "Punnet Square" for tossing two coins.

7.    Construct a "Punnet Square" for two parents, each with the gene combination NT, where N stands for normal cells and T stands for trait (sickle cell anemia) cells.

8.    If sickle cell anemia occurs only when the offspring receives the gene for T cells from both parents, find the probability that a child born to the parents in problem 7 will have sickle cell anemia.

9.    The child will carry the trait but not have the disease if a normal cell combines with a trait cell. Find the probability of this occurrence for the parents in 7.

10.    Given that the gene for brown eyes is dominant over the gene for blue eyes, construct a Punnet square to show the expected eye color in children whose father has pure brown eyes and whose mother has blue eyes.
 
 
 
 
 
 

Genetics Problems

1.    Right-handedness is a dominant trait over left handedness. Is it possible for a left-handed couple to have a (biological) child who is right handed? Explain.
 
 
 

2.    The trait of having free earlobes is dominant over having attached earlobes. Sally Smith has free earlobes. What conclusions can we make about her (biological) parents?
 
 
 

3.    Sally's brother Sam has attached earlobes. What if any information does this give you about their parents (Sally and Sam have the same biological parents)?
 
 
 

4.    Hair curl works differently from the traits we've studied so far. Very curly hair, C, is dominant over very straight hair, c. But if you are Cc for hair curl, your hair will be wavy.  If 2 wavy haired people have a child, what is the probability that the child's hair will be          a) wavy?          b) very curly?          c) very straight?
 
 
 

5.    Is it possible for a biological child of a colorblind father and a mother with normal vision to have normal vision? Explain.