Final answer:
The coefficient of relatedness between a great uncle and his great-niece is 1/4 or 25%, indicating that they share 25% of their genes by common descent, calculated using the product rule of probability. so, among the given options, option 1 is the correct answer.
Step-by-step explanation:
The coefficient of relatedness between a great uncle and his great-niece is the proportion of genes they can be expected to share by common descent. To determine this coefficient, we need to understand that each parent passes half of their genes to their offspring. A niece inherits ½ of her genes from her parent, who in turn inherited ½ from the great uncle.
Therefore, the coefficient of relatedness is ⅔ (or 0.25), which can also be understood as a 25% chance that a given gene in the great-niece is identical by descent to a gene in the great uncle. This uses the product rule of probability, which multiplies the probability of each independent event.