Directional selection is a process of natural selection when a single phenotype is chosen over another, and thus, many of the organisms in the population are phenotype instead of another extreme. 

An allele is the specific gene out of many for a given trait. The genotype is the combination of alleles that are present in the individual.

A homozygous individual expresses the same two alleles for a given trait. An example would be a person with blue eyes would have two recessive alleles for that eye color, bb.

Using a pungent square, one can determine that 1/2 will have genotype Tt and will be tall, 1/4 will have genotype TT and will also be tall, 1/4 will have genotype tt and will be short.

         T          t

T     TT        Tt

t      Tt        tt

Using a punnet square, we can see that:1/4 will be red with long pedals, 1/4 will be red with short pedals, 1/4 will be white with long pedals, and 1/4 will be white with short pedals.

     RL     Rl       rL       rl

rl RrLl     Rrll      rrLl      rrll

A lethal gene is any gene that, when expressed with another lethal gene, can cause death in an individual. It can be dominant or recessive in nature.

Founder effect is when a few individuals from a population are moved to a different environment and over generations, their genetic makeup differs from their original population. 

A bottleneck effect would require most of the population to die from natural cause, instead of being moved. Independent assortment has to do with alleles and hence is not relevant. Both non-random mating and genetic drift would not cause a change in the genetic makeup of the population. 

The question asks us to think about offspring with black horns in a trio formation. That means these offspring would be showing a recessive trait for coloration (black) and a dominant trait for arrangement (three horns). Since only one dominant allele is required for a dominant trait to "show through," the horn arrangement gene must have at least one dominant allele, which we can write as T[ ]. However, for a recessive trait to be displayed, both alleles must be recessive: therefore, these offspring need to have ww for coloration. Thus, we are concerned with those offspring that have a genotype of T[ ]ww– that is, offspring with genotypes TTww or Ttww.

We already are given one parent's genome in the question itself: "heterozygous for both traits" means this alien has one dominant and one recessive allele for each gene. Thus, the known parent's genotype is TtWw. We can first eliminate any answer choices that can't result in any three-black-horned babies at all. The known parent has a dominant allele for horn arrangement, meaning that there is at least some chance of this parent's children having three horns, no matter who s/he mates with. We should thus focus our energy more towards looking at the possibility of black-horned babies. If this parent mated with another alien who had only dominant genes on the coloration gene, then all their children would inherit at least one dominant gene for coloration (at least one W) and thus none would have a chance of having black horns. This means we can eliminate the choice with two dominant W's: the other parent won't be ttWW.

Next, let's consider a special situation in Mendelian genetics called a dihybrid cross. This is the mating of two parents who are both heterozygous for two traits. In this example, this mating would be our known parent (TtWw) crossed with another double heterozygote (another TtWw). The proportion of offspring phenotypes for a dihybrid cross is known to be 9:3:3:1. This means that for every 16 babies, we expect that nine will show both dominant traits; three will show dominant trait A and recessive trait B; three will show recessive trait A and dominant trait B; and one will show both recessive traits. We're concerned with those offspring that show one dominant and one recessive trait, so that means that for TtWw x TtWw, 3 out of 16 offspring will have three black horns.

From here, we probably want to look at Punnett square for the other two parent options. For a Punnett square involving two traits, we want 16 total squares representing offspring. When writing the possible allele combinations (as one allele from trait A and one allele from trait B) each parent could donate to the child, we essentially "repeat" each allele once. That is, we write the first trait A allele twice, the second trait A allele twice, the first trait B allele twice, and the second trait B allele twice. For a TtWw x ttWw cross, this looks like:

The offspring with horns in a trio arrangement (at least one T) and black coloration (two w's) are underlined and italicized so they are easier to see. From this we can see that for TtWw x ttWw, 2 out of 16 offspring will have three black horns.

Let's do the same thing for the last answer choice for the second parent's genotype: TTww.

Wow! This means that for TtWw x TTww, 8 out of 16 offspring will have three black horns.

Now let's compare our options:

• TtWw x ttWW: 0/16 three black horns
• TtWw x TtWw: 3/16 three black horns
• TtWw x ttWw: 2/16 three black horns
• TtWw x TTww: 8/16 three black horns

Clearly, crossing with TTww gives the TtWw parent's offspring the best chance of have three black horns, so that is our correct answer.

The statement presented in the question is true of human genetics and helps explain how genetic material from both parents combines to form a child when the parents' gametes unit in fertilization. The best choice here is the Mendelian law of segregation, which essentially means the same thing as the statement provided. Two of the other choices—the laws of dominance and independent assortment—are also Mendelian laws of inheritance, but they are not directly related to the question material. They refer respectively to the ideas that the dominant version of the two versions of a gene (alleles) an individual possess will be expressed, and that genes are distributed to each gamete independently of each other so that traits on different genes are not correlated with each other.

While recombination is an important part of meiosis and thus genetic inheritance, it isn't considered a "law" per se. As a concept, it is still not the best answer choice.

All of these are correct, true statements except choice III. Random mating indeed refers to individuals mating without choosing mates based on their traits, and this allows all alleles to be passed down to the next generation at roughly the same rate; however, in reality, organisms often show non-random preferences when choosing mates. They tend to prefer mates with traits that will make them survive longer, better able to raise offspring, more capable of protecting the family group, etc. With that said, it's clear that certain individuals have a much lower chance of successively mating—for example, if they have a genetic disorder that makes them weaker or less healthy than the average member of the species.

Since individuals choose mates non-randomly, the most reproductively fit individuals pass down their genes at a significantly higher rate than other individuals. This is also called "survival of the fittest" and is a major concept tied up with natural selection. As such, choice III is incorrect, since natural selection is essentially opposite to random mating.