4: Probability Distributions
Students apply the normal distribution to calculate probabilities, use z-tables, and identify properties of probability distributions.
Hardy-Weinberg Variables from Population Data
Click to show Hardy-Weinberg Variables from Population Data example problem
In the desert population of snakes, there is a display of incomplete dominance in scale pattern. Individuals with two M alleles exhibit diamond pattern, those with one M allele and one m allele exhibit striped pattern, and those with two m alleles exhibit solid color.
A group of 10000 snakes were observed. 7921 exhibited the diamond pattern scale pattern, 1958 had the striped pattern scale pattern, and 121 showed the recessive form of solid color scale pattern.
Which Hardy-Weinberg variable is represented by the fraction
| 7,921 |
| 10,000 |
Which Hardy-Weinberg variable is represented by the fraction 7921/10000?
Hardy-Weinberg Allele and Genotype Frequencies from Population Data (Numeric)
Click to show Hardy-Weinberg Allele and Genotype Frequencies from Population Data (Numeric) example problem
| frogs | ||
|---|---|---|
| genotype | phenotype | count |
| homozygous dominant | red | 10,329 |
| heterozygous | violet | 12,342 |
| homozygous recessive | blue | 2,329 |
| SUM | 25,000 | |
In a field there are 10,329 red frogs, 12,342 violet frogs, and 2,329 blue frogs that show incomplete dominance. What is the frequency of the dominant allele?
Note: Do not enter a percentage on the blank. For example, if the answer is 85.4%, enter 0.854 on the blank. Your answer will be a decimal value between 0 and 1.
Parent Genotypes in X-Linked Recessive Crosses
Click to show Parent Genotypes in X-Linked Recessive Crosses example problem
The white-eyed (mutant) phenotype is an X-linked recessive disorder in fruit flies. The red-eyed (wildtype) allele, +, is dominant to the white (mutant) allele, w. The offspring of size 160 from the mating of a single female (♀) and a single male (♂) are shown in the table below:
| phenotype | female (♀) | male (♂) |
|---|---|---|
| red-eyed (wildtype) | 82 | 34 |
| white-eyed (mutant) | 0 | 44 |
What are the genotypes of the parents in this cross?
Offspring Sex Distribution Using the Binomial Model
Click to show Offspring Sex Distribution Using the Binomial Model example problem
Model: Binomial →
| ⟮ | n | ⟯ |
| k |
In this scenario, assume that each child is born independently with the same chance of being either sex. The event outcomes are mutually exclusive, so we can apply the binomial model to determine the probability of a specific combination.
A woman has nine (9) children. What is the probability that she has exactly seven (7) boys ♂ and two (2) girls ♀?