Ch. 14 - Mendel and the Gene Idea

Problem 7

Chapter 14, Problem 7

The genotype of F1 individuals in a tetrahybrid cross is AaBbCcDd. Assuming independent assortment of these four genes, what are the probabilities that F2 offspring will have the following genotypes? a. aabbccdd b. AaBbCcDd c. AABBCCDD d. AaBBccDd e. AaBBCCdd

Verified step by step guidance

Step 1: Understand that each gene pair (Aa, Bb, Cc, Dd) segregates independently during gamete formation. This means each allele has a 1/2 chance of being passed on to the F2 generation.

Step 2: Calculate the probability for each genotype by multiplying the probabilities of obtaining each specific allele. For example, the probability of getting 'aa' from 'Aa x Aa' is (1/2 * 1/2) = 1/4.

Step 3: Apply the multiplication rule to find the probability of the genotype 'aabbccdd'. Since each gene pair is homozygous recessive, the probability is (1/4)^4 = 1/256.

Step 4: For the genotype 'AaBbCcDd', each gene pair must be heterozygous. The probability for each gene pair to be heterozygous is 1/2 * 1/2 = 1/4. Thus, the probability for 'AaBbCcDd' is (1/4)^4 = 1/256.

Step 5: Similarly, calculate the probabilities for 'AABBCCDD' (1/256), 'AaBBccDd' (1/256), and 'AaBBCCdd' (1/256), by considering the required combination of alleles for each gene.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Independent Assortment

Independent assortment is a fundamental principle of genetics stating that alleles for different genes segregate independently of one another during gamete formation. This means that the inheritance of one trait will not affect the inheritance of another, allowing for a variety of combinations in offspring genotypes.

Punnett Square

A Punnett square is a diagram used to predict the genotype and phenotype combinations of offspring from a genetic cross. By organizing the possible gametes from each parent, it allows for a visual representation of the probabilities of different genotypes in the offspring, making it easier to calculate expected ratios.

Genotype Probability Calculation

Calculating genotype probabilities involves determining the likelihood of specific allele combinations in offspring based on parental genotypes. For a tetrahybrid cross like AaBbCcDd, the probability of each genotype can be calculated by multiplying the probabilities of each individual gene's alleles, considering their independent assortment.

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