Final answer:
The probability that a randomly selected woman carries the mutation of the particular gene is 1/500.
Step-by-step explanation:
The probability that a randomly selected woman carries the mutation of the particular gene can be calculated using the given information. The rate of mutation for this gene is estimated to be 1 in 100,000. So, out of a large group of women, approximately 1 in 500 or 0.002 (0.2%) would carry this mutation.
To calculate the probability, we divide the number of women carrying the mutation (1) by the total number of women in the group (500). Therefore, the probability is 1/500.