In guinea pigs, black fur (B) is dominant over white fur (b). If two heterozygous black gu… — Armed Services Vocational Aptitude Battery (ASVAB)

In guinea pigs, black fur ( $B$ ) is dominant over white fur ( $b$ ). If two heterozygous black guinea pigs ( $Bb$ ) produce an offspring with black fur, what is the probability that this offspring is heterozygous?

A
$\frac{1}{2}$
$\frac{2}{3}$ Answer
C
$\frac{3}{4}$
D
$\frac{1}{4}$

Answer

\frac{2}{3}

A monohybrid cross of two heterozygous parents (

Bb \times Bb

) yields four equally likely outcomes:

1\,BB

2\,Bb

, and

1\,bb

. Because the problem specifies that the offspring has black fur, the homozygous recessive genotype (

bb

) is excluded. Among the remaining three dominant outcomes (

1\,BB

and

2\,Bb

), two are heterozygous, giving a probability of

\frac{2}{3}

Step-by-Step Solution

Determine all possible genotypes from crossing two heterozygous individuals (

Bb \times Bb

The genotypic ratio of the total offspring is

1\,BB : 2\,Bb : 1\,bb

Each heterozygous parent contributes either a dominant allele (

B

) or a recessive allele (

b

) with equal likelihood.

Apply the given condition that the offspring displays black fur (the dominant phenotype).

The recessive genotype (

bb

) is ruled out, restricting the sample space to

1\,BB

and

2\,Bb

(a total of

3

possible outcomes).

A white guinea pig (

bb

) cannot be the offspring in question because the problem states the offspring has black fur.

Calculate the probability that this black offspring possesses the heterozygous genotype (

Bb

\text{Probability} = \frac{2\text{ heterozygous outcomes}}{3\text{ total black outcomes}} = \frac{2}{3}

There are

2

heterozygous outcomes (

Bb

) out of the

3

possible dominant phenotype outcomes (

BB, Bb, Bb

Key Concept

Conditional Probability in Monohybrid Inheritance and Phenotypic Selection

Estimated Time:1m 0s

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