Bacillus thuringiensis $($Bt$),$ a common soil bacterium, produces a crystal protein that is lethal to some lepidopteran larvae, but harmless to other organisms, including humans. Bt has been used as a biopesticide by both organic and conventional farmers for more than a century. More recently, a gene encoding the crystalline protein has been engineered into a variety of crops, including cotton.$$

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If a cotton plant is heterozygous for the Bt gene $($one homolog contains the gene, the other does not$),$ what proportion of sperm would carry the Bt gene? In this same plant, is expression of the Bt gene from one homolog dominant or recessive to its absence on the other homolog?

$1/4$; recessive

$1/4$; dominant

$1/2$; recessive

$1/2$; dominant

$3/4$; recessive

$3/4$; dominant