The frequency of the m allele of the f1 progeny is going to be 3/4.
Here, it has been mentioned in the question that the M allele is lethal, which then means that a MM genotype is going to be lethal. For an offspring to be tailless, it needs to have the genotype mm. And a wild-type cat has the genotype Mm.
It has also been given that in the population, the Manx cats and wild cats live in a ratio of 2:3. On average, 1 long-tailed cat is there for every 2 Manx. Now, after the f1 generation is produced, the genotypes are going to be - (MM, Mm, Mm, mm).
Since we know that there are 2 Manx cats (mm) for every long-tailed one (Mm), the frequency of the m allele is going to be 3/4.
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