In cattle (*Bos taurus*), the polled (hornless) condition (P) is dominant to the horned co… — JAMB UTME

In cattle (*Bos taurus*), the polled (hornless) condition ( $P$ ) is dominant to the horned condition ( $p$ ), and black coat color ( $B$ ) is dominant to red coat color ( $b$ ). If a heterozygous polled, heterozygous black bull ( $PpBb$ ) is crossed with a horned, heterozygous black cow ( $ppBb$ ), what proportion of the offspring is expected to display the horned, black coat phenotype?

$\frac{3}{8}$ Answer
B
$\frac{9}{16}$
C
$\frac{1}{4}$
D
$\frac{1}{8}$

Answer

The expected proportion of offspring displaying the horned, black coat phenotype is

\frac{3}{8}

According to Mendel's Law of Independent Assortment, the inheritance of horn condition and coat color are independent events. The cross between

Pp

and

pp

yields a

\frac{1}{2}

probability of horned offspring (

pp

). The cross between

Bb

and

Bb

yields a

\frac{3}{4}

probability of black-coated offspring (

BB

Bb

). Multiplying these independent probabilities (

\frac{1}{2} \times \frac{3}{4}

) gives

\frac{3}{8}

as the expected fraction of horned, black-coated offspring.

Step-by-Step Solution

Analyze the cross for the horn condition trait independently.

The cross

Pp \times pp

produces genotypes

Pp

(polled) and

pp

(horned) in a

1:1

ratio, giving a probability of

P(pp) = \frac{1}{2}

Mendel's Law of Segregation dictates that alleles segregate independently into gametes.

Analyze the cross for the coat color trait independently.

The cross

Bb \times Bb

produces phenotypes in a

3:1

ratio, giving a probability of

P(\text{black coat}, B\_) = \frac{3}{4}

Crossing two heterozygotes results in

\frac{1}{4} BB

\frac{1}{2} Bb

, and

\frac{1}{4} bb

genotypes.

Combine the independent probabilities using Mendel's Law of Independent Assortment.

P(\text{horned and black coat}) = P(pp) \times P(B\_) = \frac{1}{2} \times \frac{3}{4} = \frac{3}{8}

Because the two gene pairs assort independently, the combined probability is the product of their separate probabilities.

Key Concept

Mendel's Law of Independent Assortment and Probability Calculations in Dihybrid Crosses

Estimated Time:1m 30s

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