Chapter 3 Online Worked Problem: Statistics and Probability
Problem Statement
Individuals with the following genotypes are crossed: Aa Bb Cc Dd x Aa Bb Cc Dd. Alleles of these four genes/loci assort independently of one another. Give the proportion of the progeny of this cross that are expected to have each of the following genotypes:
a) Aa Bb Cc Dd
b) aa bb cc dd
c) Aa Bb cc Dd
For help with this problem:
Review Predicting the Outcomes of Genetic Crosses on Pages 53-57 of Section 3.2 and Applying Probability and the Branch Diagram on Pages 61-62 in Section 3.3.
Review Figures 3.12 and 3.13 on Pages 61-62.
Review the Worked Problem on Pages 62-63.
Question
Begin by thinking about the steps to take to do this problem. Use the dropdown menu to put the steps in the order in which they should be performed.
Use the multiplication rule to calculate the probabilities of the requested genotype combinations.
Choose a problem-solving approach.
Identify the question being asked.
Define terms you may not know or understand.
Identify relevant information in the problem that will enable you to answer the question.
For each of the four loci, calculate the probabilities of each possible genotype among the progeny.
2
Correct.
Incorrect. You have one more chance to answer correctly. Review the Instant TA and try again.
It is always good practice to first define any unfamiliar terms. Next, you’ll need to identify the question that is being asked and figure out what information is available to help you answer the question. Before performing calculations, it is best to choose a problem-solving approach. In problems that ask for combined probabilities, you’ll need to calculate individual probabilities first and then use the multiplication rule with those individual probabilities to calculate the combined probabilities.
Instant TA
Do you understand all the terms used in the question? What question is being asked? What would you do next after figuring out these first two steps? For the last two steps, which needs to be calculated before the other: individual probabilities or combined probabilities?
Step 1: Define terms you may not know or understand.
Question
Choose the correct statement.
A.
B.
C.
D.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Review the definitions of genes, alleles, and locus/loci in your text. See Table 3.1 on Page 48.
Step 2: Identify the question being asked.
Question
What problem are you being asked to solve?
A.
B.
C.
D.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Are you given genotype or phenotype information in the question? Are you being asked to figure out the geno-/phenotypes or their proportions?
Step 3: Identify the information provided that will enable you to answer the question.
Question
What information will help you to solve the problem?
A.
B.
C.
D.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Are you given genotype or phenotype information in the question? Are you being asked to figure out the geno-/phenotypes or their proportions?
Step 4: Choose a problem-solving approach.
Question
What approach will help you to solve this problem?
A.
B.
C.
D.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Consider the type of cross that is involved in this problem. It is not a monohybrid or dihybrid cross, so some problem-solving approaches will not be practical. Next, determine whether you should use the multiplication rule or the addition rule to calculate the requested combined genotypic frequencies. Finally, determine if you need to test whether the expected and observed values are statistically significantly different using a chi-square goodness-of-fit test.
Step 5: For each of the four loci, calculate the probabilities of each possible genotype among the progeny.
Question
1. What are the genotypes of the parents with respect to locus 1 (i.e., alleles A/a)?
A.
B.
C.
D.
E.
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
This information is given in the problem statement. Reread it if you’re unsure of the answer.
Question
2. What are the genotype frequencies among the offspring with respect to locus 1 (i.e., alleles A/a):
A.
B.
C.
D.
E.
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
Because this part of the problem is a simple monohybrid cross, you can draw a small Punnett square to calculate the probabilities for this locus alone.
A
a
A
AA
Aa
a
Aa
aa
Question
3. What are the genotypes of the parents with respect to locus 2 (i.e., alleles B/b)?
A.
B.
C.
D.
E.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
This information is given in the problem statement. Reread it if you’re unsure of the answer.
Question
4. What are the genotype frequencies among the offspring with respect to locus 2(i.e., alleles B/b):
A.
B.
C.
D.
E.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Because this part of the problem is a simple monohybrid cross, you can draw a small Punnett square to calculate the probabilities for this locus alone.
B
b
B
BB
Bb
b
Bb
bb
Question
5. What are the genotypes of the parents with respect to locus 3 (i.e., alleles C/c)?
A.
B.
C.
D.
E.
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
This information is given in the problem statement. Reread it if you’re unsure of the answer.
Question
6. What are the genotype frequencies among the offspring with respect to locus 3 i.e., alleles C/c):
A.
B.
C.
D.
E.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Because this part of the problem is a simple monohybrid cross, you can draw a small Punnett square to calculate the probabilities for this locus alone.
C
c
C
CC
Cc
c
Cc
cc
Question
7. What are the genotypes of the parents with respect to locus 4 (i.e., alleles D/d)?
A.
B.
C.
D.
E.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
This information is given in the problem statement. Reread it if you’re unsure of the answer.
Question
8. What are the genotype frequencies among the offspring with respect to locus 4i.e., alleles D/d):
A.
B.
C.
D.
E.
2
Correct.
Incorrect.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Instant TA
Because this part of the problem is a simple monohybrid cross, you can draw a small Punnett square to calculate the probabilities for this locus alone.
D
d
D
DD
Dd
d
Dd
dd
Step 6: Use the multiplication rule to calculate the probabilities of the requested genotype combinations.
Question
1. For the first requested genotypic combination of Aa Bb Cc Dd, use the proportions you calculated for each locus in step 5 to calculate the combined proportion among the offspring. Use fractions (e.g., 1/256) rather than decimals to do your calculations.
probability of Aa among offspring
x probability of Bb among offspring
x probability of Cc among offspring
x probability of Dd among offspring
= combined probability of Aa Bb Cc Dd
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
Be sure you use the specific probability for each of the genotypes that are requested in the problem. Use the multiplication rule to calculate the combined probability.
Question
2. For the second requested genotypic combination of aa bb cc dd, use the proportions you calculated for each locus in step 5 to calculate the combined proportion among the offspring. Use fractions rather than decimals to do your calculations.
probability of aa among offspring
x probability of bb among offspring
x probability of cc among offspring
x probability of dd among offspring
= combined probability of aa bb cc dd
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
Be sure you use the specific probability for each of the genotypes that are requested in the problem. Use the multiplication rule to calculate the combined probability. Follow the same process you used in question 1 directly above.
Question
3. For the third requested genotypic combination of Aa Bb cc Dd, use the proportions you calculated for each locus in step 5 to calculate the combined proportion among the offspring.
probability of Aa among offspring
x probability of Bb among offspring
x probability of cc among offspring
x probability of Dd among offspring
= combined probability of Aa Bb cc Dd
2
Correct.
Incorrect. You have one more chance to answer correctly. Please review the feedback above and try again.
Incorrect.
Instant TA
Be sure you use the specific probability for each of the genotypes that are requested in the problem. Use the multiplication rule to calculate the combined probability. Follow the same process you used in questions 1 & 2 directly above.