Question

What is the probability that each of the following pairs of parents will produce the indicated offspring? (Assume independent assortment of all gene pairs)

(a)$AABBCC\times aabbcc\to AaBbCc$

(b) $AABbCc\times AaBbCc\to AAbbCC$

(c)$AaBbCc\times AaBbCc\to AaBbCc$

(d) $aaBbCC\times AABbcc\to AaBbCc$

Short answer

(a) The probability for the pair $AABBCC\times aabbcc\to AaBbCc$is 1.

(b) The probability for the pair $AABbCc\times AaBbCc\to AAbbCC$is 1/32.

(c) The probability for the pair $AaBbCc\times AaBbCc\to AaBbCc$is 1/8.

(d) The probability for the pair $aaBbCC\times AABbcc\to AaBbCc$is 1/2.

Step-by-step solution

Independent assortment

The development of reproductive cells involves the separation of chromosomes. The independent assortment is the concept that deals with the separation of chromosomes that takes place differently.

Explanation for part “a”

The probability of the homozygous dominant traits or heterozygous recessive traits is 1. The offspring with the trait combination is given as AaBbCc, so the probability is calculated as follows:

Probability= $1\times 1\times 1$role="math" localid="1643627680032" $=1$

Explanation for part “b”

The probability of the homozygous AA is 25% or 1/4 as per the independent assortment. The probability of heterozygous bb is 50% or ½, and for a homozygous recessive trait, CC is 25% or ¼. The overall probability of the given pairs is calculated as follows:

Probability=$1/2\times 1/4\times 1/4=1/32$

Explanation for part “c”

The probability of the heterozygous trait Aa is 50% or 1/2 as per the independent assortment. The probability of heterozygous Bb is 50% or ½, and heterozygous trait Cc is 50% or ½. The overall probability of the given pairs is calculated as follows:

Probability=$1/2\times 1/2\times 1/2=1/8$

Explanation for part “d”

The probability of the homozygous dominant trait Aa is 100% or one as per the independent assortment. The probability of heterozygous Bb is 50% or ½. The probability of heterozygous recessive trait Cc is 100% or 1. The overall probability of the offspring with given pairs is calculated as follows:

Probability=$1\times 1/2\times 1=1/2.$