In sorghum plants, tall stem height (T) is completely dominant over dwarf stem height (t).… — JAMB UTME

In sorghum plants, tall stem height ( $T$ ) is completely dominant over dwarf stem height ( $t$ ). In a monohybrid cross between two heterozygous tall plants ( $Tt \times Tt$ ), the conditional probability that a plant displaying the tall phenotype is homozygous dominant ( $TT$ ) is $1/3$ .

Answer: Answer

Answer

The statement is true because restricting the sample space to offspring displaying the dominant tall phenotype (

TT

and

Tt

) yields 3 out of 4 total genotypic combinations, of which exactly 1 is homozygous dominant (

TT

), giving a conditional probability of

1/3

The statement is correct because out of the 3 possible genotype combinations that produce the dominant tall phenotype (

1\ TT

and

2\ Tt

), exactly 1 is homozygous dominant (

TT

), making the conditional probability

1/3

Step-by-Step Solution

Determine the genotypic ratio resulting from a monohybrid cross of two heterozygotes (

Tt \times Tt

The genotypic ratio is

1\ TT : 2\ Tt : 1\ tt

According to Mendel's Law of Segregation, alleles segregate independently during gamete formation, resulting in a

1:2:1

genotypic ratio.

Identify the genotypes that express the dominant tall phenotype.

Tall plants possess either the homozygous dominant genotype (

TT

) or the heterozygous genotype (

Tt

), totaling

3

out of

4

genotypic units (

1\ TT + 2\ Tt

Dominance dictates that both

TT

and

Tt

produce the tall phenotype.

Calculate the conditional probability that a tall plant is homozygous dominant (

TT

The probability is

\frac{\text{Number of } TT \text{ combinations}}{\text{Total number of tall combinations}} = \frac{1}{1 + 2} = \frac{1}{3}

The question restricts the sample space to only tall offspring.

Key Concept

Conditional probability in monohybrid crosses and Mendel's Law of Segregation

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