Question

blond hair is an inherited recessive trait. the punnett square shows the genetic cross for blond hair in the smith family. if the smiths have six children, how many could be blond?
a 0
b 1
c 2
d 3

Explanation:

Step1: Analyze Punnett Square

The Punnett square for blond hair (recessive trait, let's say allele \( a \)): From the square, the probability of a child having blond hair (genotype \( aa \)) is \( \frac{1}{4} \)? Wait, no, looking at the square (assuming the cross is, say, \( Aa \times Aa \)? Wait, the square has cells: let's parse the Punnett square. The rows and columns: suppose one parent is \( Aa \) and the other? Wait, the square shows: top row maybe \( A, A \), left column \( A, a \)? Wait, no, the given Punnett square (as per image) has cells with \( Aa, Aa, aa, aa \)? Wait, maybe the cross is \( Aa \times aa \)? Wait, no, let's re-express. Wait, the problem says blond hair is recessive (\( aa \)). Let's look at the Punnett square: if the square has, for example, two \( Aa \) and two \( aa \)? Wait, no, the user's image: the Punnett square has 4 cells? Wait, the text says "the Punnett square shows the genetic cross for blond hair". Let's assume that the probability of a child being blond (aa) is \( \frac{1}{2} \)? Wait, no, let's check the options. The Smiths have 6 children. The options are 0,1,2,3. Wait, maybe the Punnett square gives a 50% chance? Wait, no, let's think again. Wait, if blond is recessive (aa), and the Punnett square shows that 2 out of 4 (50%) are aa? Wait, no, maybe the cross is \( Aa \times aa \), so the Punnett square would have 2 Aa and 2 aa, so probability of aa is \( \frac{2}{4} = \frac{1}{2} \). Then for 6 children, expected number is \( 6 \times \frac{1}{2} = 3 \)? Wait, no, the options include 3 (D), 2 (C), 1 (B), 0 (A). Wait, maybe the Punnett square has 1 out of 4? No, that would be 1.5, not an option. Wait, maybe the cross is \( Aa \times Aa \), then probability of aa is \( \frac{1}{4} \), 6 1/4 = 1.5, not option. Wait, maybe the Punnett square is \( AA \times aa \)? No, that would be all Aa, 0 blond. No. Wait, maybe the square shows that 2 out of 4 are aa (50% chance). So 6 children: 6 0.5 = 3? But option D is 3. Wait, but let's check the problem again. The question is "how many could be blond?" So it's the expected number or possible? Wait, the options are 0,1,2,3. Let's re-express: if the Punnett square has a 25% chance (1/4), 61/4=1.5, not integer. If 50% (1/2), 61/2=3. So maybe the Punnett square has 2 out of 4 (50%) as aa. So the probability is 1/2. Then 6 children: 6 * 1/2 = 3. So the answer is D (3).

Step2: Calculate Expected Number

If the probability of a child being blond is \( p \), then expected number is \( n \times p \), where \( n = 6 \). From the Punnett square, suppose \( p = \frac{1}{2} \) (e.g., cross \( Aa \times aa \), giving 2 aa out of 4). Then \( 6 \times \frac{1}{2} = 3 \).

Answer:

D. 3