Step 1: Understand the haplodiploid system.
In haplodiploid species such as honey bees, sex is determined by the number of chromosome sets inherited.
Females (workers and queens) are diploid and develop from fertilized eggs, while males (drones) are haploid and arise from unfertilized eggs.
As a result, male bees possess only one set of chromosomes, all of which come from their mother.
Step 2: Compute genetic relatedness between sisters.
Two sister bees receive genetic material from both parents:
They share, on average, half of their maternal genes, since maternal alleles are randomly passed on.
They also receive identical genetic material from their father because he is haploid and transmits the same genome to all daughters.
The total relatedness between sisters is therefore:
\[ r = \frac{1}{2} \times 0.5 + \frac{1}{2} \times 1 = 0.25 + 0.5 = 0.75 \]
Step 3: Consider the other pairings.
Brother–brother pairs are less closely related because brothers arise from unfertilized eggs and do not share a father.
Brother–sister pairs share genes only through their mother, giving a relatedness of 0.25.
A mated female–male pair has no genetic relatedness, as mates are unrelated.
Step 4: Final conclusion.
In haplodiploid organisms like honey bees, the unusually high relatedness value of 0.75 is found between:
\[ \boxed{\text{sister–sister pairs with the same parents}} \]