Question

In a dihybrid cross AaBb × AaBb, what percentage of offspring will show at least one recessive trait?

• A. 25%
• B. 37.5%
• C. 43.75%
• D. 50%

Hint:

Key Fact: In genetics, use the product rule for independent traits and the complement rule for “at least” probabilities.

Answer 1

The Correct Option is C

Step 1: Determine Total Combinations
In a dihybrid cross AaBb × AaBb, each trait (A and B) segregates independently. Total offspring combinations = \( 4 \times 4 = 16 \).

Step 2: Find Offspring with No Recessive Traits
For each trait: - Probability of not having recessive \( a \): \( P(\text{AA or Aa}) = \frac{3}{4} \) - Probability of not having recessive \( b \): \( P(\text{BB or Bb}) = \frac{3}{4} \) - Probability of no recessive traits: \[ P(\text{no recessive}) = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} \]

Step 3: Calculate Probability of At Least One Recessive Trait
\[ P(\text{at least one recessive}) = 1 - P(\text{no recessive}) = 1 - \frac{9}{16} = \frac{7}{16} \]

Step 4: Convert to Percentage
\[ \frac{7}{16} \times 100 = 43.75% \]