Final answer:
The probability that a female honeybee will inherit the recessive allele from a heterozygous queen is 0.5. For male honeybees, the probability of inheriting a recessive allele from the heterozygous queen is also 0.5. Hence, the correct answer is option b.
Step-by-step explanation:
In the haplo-diploid sex determination system of honeybees, females develop from fertilized eggs and are diploid, whereas males originate from unfertilized eggs and are haploid. Given that a queen bee is heterozygous for a given gene, we can determine the probability of an offspring inheriting a recessive allele using Mendelian genetics principles.
For a female offspring (worker bee), the mother (queen bee) contributes two alleles, one of which may be recessive. If the queen is heterozygous (Bb), there is a 50% chance (1 in 2) that a given female offspring will inherit the recessive allele (b). Therefore, the probability is 0.5.
For a male offspring (drone), the male develops from an unfertilized egg, thus receiving only one allele from the mother. If the queen is heterozygous (Bb), there is still a 50% chance that a drone will inherit the recessive allele from her. Consequently, the probability is also 0.5.
The correct option in both parts is option b: the Probability of female inheriting a recessive allele = 0.5 and the Probability of male inheriting a recessive allele = 0.5.