For a single dice roll, there is a 1/6 chance that any particular number will appear. For a pair of dice, each specific combination of numbers has a probability of 1/36 occurring. Most total values of two dice can occur more than one way. As a test of random probability theory, a student decides to roll a pair of six-sided dice 300 times and tabulate the results. She tabulates the number of times each different total value of the two dice occurs. Her results are the following:

Total Value of Two Dice      Number of Times Rolled
               2                                          7
               3                                         11
               4                                         23
               5                                         36
               6                                         42
               7                                         53
               8                                         40
               9                                         38
              10                                        30
              11                                        12
              12                                         8
           TOTAL                                   300

The student tells you that her results fail to prove that random chance is the explanation for the outcome of this experiment. Is she correct or incorrect? Support your answer.

Two parents who are each known to be carriers of an autosomal recessive allele have four children. None of the children has the recessive condition. What is the probability that one or more of the children is a carrier of the recessive allele?

A man and a woman are each heterozygous carriers of an autosomal recessive mutation of a disorder that is fatal in infancy. They both want to have multiple children, but they are concerned about the risk of the disorder appearing in one or more of their children. In separate calculations, determine the probabilities of the couple having five children with 0, 1, 2, 3, 4, and all 5 children being affected by the disorder.

In a breed of domestic cattle, horns can appear on males and on females. Males and females can also be hornless. The following crosses are performed with parents from pure-breeding lines.

Explain the inheritance of this phenotype in cattle, and assign genotypes to all cattle in each cross.

Cross 1 shown in Figure 4.22 illustrates genetic complementation of flower-color mutants. The  produced from this cross of two pure-breeding mutant parental plants are dihybrid (CcPp) and have wild-type flower color. If these F₁ are allowed to self-fertilize, what phenotypes are expected in the F₂  and what are the expected ratios of the phenotypes?

The wild-type allele of a gene has an A–T base pair at a particular location in its sequence, and a mutant allele of the same gene has a G–C base pair at the same location. Otherwise, the sequences of the two alleles are identical. Does this information tell you anything about the dominance relationship of the alleles? Explain why or why not.

Galactosemia is an autosomal recessive disorder caused by the inability to metabolize galactose, a component of the lactose found in mammalian milk. Galactosemia can be partially managed by eliminating dietary intake of lactose and galactose. Amanda is healthy, as are her parents, but her brother Alonzo has galactosemia. Brice has a similar family history. He and his parents are healthy, but his sister Brianna has galactosemia. Amanda and Brice are planning a family and seek genetic counseling. Based on the information provided, complete the following activities and answer the questions.

If the first child has galactosemia, what is the probability that the second child will have galactosemia? Explain the reasoning for your answer.