Question

In a trihybrid cross involving three different genes (\( AaBbCc \times AaBbCc \)), what is the expected genotypic ratio among the offspring?

• A. \( 1:1:1:1:1:1:1:1 \)
• B. \( 27:9:9:9:3:3:3:1 \)
• C. \( 64:16:16:16:16:4:4:4:1 \)
• D. \( 81:27:27:27:27:9:9:9:9:3:3:3:1 \)

Hint:

For dihybrid and trihybrid crosses, the phenotypic ratios can be derived using the expansion of \( (3+1)^n \), where \( n \) is the number of genes.

Answer 1

The Correct Option is B

Step 1: Understanding the trihybrid cross.
The given cross involves three genes (\( A, B, C \)) that segregate independently according to Mendel's law of independent assortment. Each parent (\( AaBbCc \)) is heterozygous for all three genes. Step 2: Determining the phenotypic ratio.
For a trihybrid cross, the phenotypic ratio can be calculated using the following rule: \[ (3 + 1)(3 + 1)(3 + 1) = 64 \text{ phenotypes}. \] The phenotypic ratio is split based on the dominance and recessive nature of the alleles: \[ 27:9:9:9:3:3:3:1. \] Step 3: Explanation of the ratio.
- \( 27 \): All dominant traits (\( A\_B\_C\_ \)). - \( 9 \): Two dominant and one recessive trait (\( A\_B\_cc, A\_bbC\_, aaB\_C\_ \)). - \( 3 \): One dominant and two recessive traits (\( A\_bbcc, aaB\_cc, aabbC\_ \)). - \( 1 \): All recessive traits (\( aabbcc \)). Thus, the final phenotypic ratio is: \[ \boxed{27:9:9:9:3:3:3:1}. \]